Since you did not show the output you expect, I wonder if you really want HASHES OF ARRAYS:

use warnings;
use strict;
use Data::Dumper;

my @lines = <DATA>;

my $n;
my %all_hash;
for (@lines) {
        chomp;
        if (/^>/) {
                $n = $_;
        } else {
                push @{ $all_hash{ $n } }, $_;
        }
}       
print Dumper(\%all_hash);

__DATA__
>seq1
ASDFGHASDFGHJ
ERTYUIOOIUYLK
NBGFEWERTY
>seq2
BGTNHYMJUKOPK
MNBFSDFGHJ
[download]

Prints:

$VAR1 = {
          '>seq1' => [
                       'ASDFGHASDFGHJ',
                       'ERTYUIOOIUYLK',
                       'NBGFEWERTY'
                     ],
          '>seq2' => [
                       'BGTNHYMJUKOPK',
                       'MNBFSDFGHJ'
                     ]
        };
[download]