Try the following:

use strict;
use warnings;

my $i = 1;

while (<>) {
    s/>\K.+/$i++/e;
    print;
}
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Output from your data:

>1

MNLTFDYTKEPSRDVLCIDVKSFYASVECVERG LDPLKTMLVVMSNSENSGGLVLAASPM

>2

MKQNRKEFSSYFSRSIKQNKPLYLLLMSSETNPF PRPVIGTFRGYVEENKIIIGEDSYSI
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Usage: perl script.pl inFile >outFile

As the fasta inFile is read line-by-line, the regex will substitute all past the > with the value of $i. The >outFile notation directs the printing to the file outFile.

Hope this helps!