See perlvar $INPUT_RECORD_SEPARATOR.

#! perl -slw
use strict;
use Data::Dumper;

local $/ = '>'; # Set record delimiter

my @sequences; # AoA

(undef) = scalar <DATA>; # Discard first (blank) record.

while( my $record = <DATA> ) { # Read each paragraph

    # Split to lines
    my @lines = split "\n", $record;

    # Discard the last line if necessary
    pop @lines if $lines[-1] eq '>';

    # Build the array
    push @sequences, [ split( '\|', shift @lines), join( '', @lines ) 
+];
}

print Dumper \@sequences;

__DATA__
>gi|2695846|emb|Y13255.1|ABY13255 Acipenser baeri mRNA for immunoglobu
+lin heavychain, clone ScH 3.3
TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTTAACAGCTCTCTGT
+ATAATAATGA
CAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGGACCAGCAGTTATAAAGCCTGGAGA
+GTCCCATAAA
CTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAGCGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAA
+AGGGTCTGGA
ATGGGTGGCTTATATTTACTCAGGTGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCC
+ATCTCCAGAG
ACGATTCCAACAGCATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTG
+TGCTCGGGGC
GGGCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCAC
+CACCGACAGT
GTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTGCTTAGCAACC
+GGATTCTGCC
TACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT
>gi|2695846|emb|Y13255.1|ABY13255 Acipenser baeri mRNA for immunoglobu
+lin heavychain, clone ScH 3.3
TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTTAACAGCTCTCTGT
+ATAATAATGA
CAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGGACCAGCAGTTATAAAGCCTGGAGA
+GTCCCATAAA
CTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAGCGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAA
+AGGGTCTGGA
ATGGGTGGCTTATATTTACTCAGGTGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCC
+ATCTCCAGAG
ACGATTCCAACAGCATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTG
+TGCTCGGGGC
GGGCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCAC
+CACCGACAGT
GTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTGCTTAGCAACC
+GGATTCTGCC
TACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT
>gi|2695846|emb|Y13255.1|ABY13255 Acipenser baeri mRNA for immunoglobu
+lin heavychain, clone ScH 3.3
TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTTAACAGCTCTCTGT
+ATAATAATGA
CAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGGACCAGCAGTTATAAAGCCTGGAGA
+GTCCCATAAA
CTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAGCGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAA
+AGGGTCTGGA
ATGGGTGGCTTATATTTACTCAGGTGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCC
+ATCTCCAGAG
ACGATTCCAACAGCATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTG
+TGCTCGGGGC
GGGCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCAC
+CACCGACAGT
GTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTGCTTAGCAACC
+GGATTCTGCC
TACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT
>gi|2695846|emb|Y13255.1|ABY13255 Acipenser baeri mRNA for immunoglobu
+lin heavychain, clone ScH 3.3
TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTTAACAGCTCTCTGT
+ATAATAATGA
CAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGGACCAGCAGTTATAAAGCCTGGAGA
+GTCCCATAAA
CTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAGCGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAA
+AGGGTCTGGA
ATGGGTGGCTTATATTTACTCAGGTGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCC
+ATCTCCAGAG
ACGATTCCAACAGCATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTG
+TGCTCGGGGC
GGGCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCAC
+CACCGACAGT
GTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTGCTTAGCAACC
+GGATTCTGCC
TACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT
[download]

Output

P:\test>junk
$VAR1 = [
          [
            'gi',
            '2695846',
            'emb',
            'Y13255.1',
            'ABY13255 Acipenser baeri mRNA for immunoglobulin heavycha
+in, clone ScH 3.3',
            'TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTT
+AACAGCTCTCTGTATAATAATGACAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGG
+ACCAGCAGTTATAAAGCCTGGAGAGTCCCATAAACTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAG
+CGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAAAGGGTCTGGAATGGGTGGCTTATATTTACTCAGG
+TGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCCATCTCCAGAGACGATTCCAACAG
+CATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTGTGCTCGGGGCGG
+GCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCACC
+ACCGACAGTGTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTG
+CTTAGCAACCGGATTCTGCCTACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT'
          ],
          [
            'gi',
            '2695846',
            'emb',
            'Y13255.1',
            'ABY13255 Acipenser baeri mRNA for immunoglobulin heavycha
+in, clone ScH 3.3',
            'TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTT
+AACAGCTCTCTGTATAATAATGACAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGG
+ACCAGCAGTTATAAAGCCTGGAGAGTCCCATAAACTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAG
+CGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAAAGGGTCTGGAATGGGTGGCTTATATTTACTCAGG
+TGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCCATCTCCAGAGACGATTCCAACAG
+CATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTGTGCTCGGGGCGG
+GCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCACC
+ACCGACAGTGTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTG
+CTTAGCAACCGGATTCTGCCTACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT'
          ],
          [
            'gi',
            '2695846',
            'emb',
            'Y13255.1',
            'ABY13255 Acipenser baeri mRNA for immunoglobulin heavycha
+in, clone ScH 3.3',
            'TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTT
+AACAGCTCTCTGTATAATAATGACAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGG
+ACCAGCAGTTATAAAGCCTGGAGAGTCCCATAAACTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAG
+CGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAAAGGGTCTGGAATGGGTGGCTTATATTTACTCAGG
+TGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCCATCTCCAGAGACGATTCCAACAG
+CATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTGTGCTCGGGGCGG
+GCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCACC
+ACCGACAGTGTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTG
+CTTAGCAACCGGATTCTGCCTACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT'
          ],
          [
            'gi',
            '2695846',
            'emb',
            'Y13255.1',
            'ABY13255 Acipenser baeri mRNA for immunoglobulin heavycha
+in, clone ScH 3.3',
            'TGGTTACAACACTTTCTTCTTTCAATAACCACAATACTGCAGTACAATGGGGATTTT
+AACAGCTCTCTGTATAATAATGACAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGTCCGG
+ACCAGCAGTTATAAAGCCTGGAGAGTCCCATAAACTGTCCTGTAAAGCCTCTGGATTCACATTCAGCAG
+CGCCTACATGAGCTGGGTTCGACAAGCTCCTGGAAAGGGTCTGGAATGGGTGGCTTATATTTACTCAGG
+TGGTAGTAGTACATACTATGCCCAGTCTGTCCAGGGAAGATTCGCCATCTCCAGAGACGATTCCAACAG
+CATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACACTGCCGTGTATTACTGTGCTCGGGGCGG
+GCTGGGGTGGTCCCTTGACTACTGGGGGAAAGGCACAATGATCACCGTAACTTCTGCTACGCCATCACC
+ACCGACAGTGTTTCCGCTTATGGAGTCATGTTGTTTGAGCGATATCTCGGGTCCTGTTGCTACGGGCTG
+CTTAGCAACCGGATTCTGCCTACCCCCGCGACCTTCTCGTGGACTGATCAATCTGGAAAAGCTTTT'
          ]
        ];
[download]