Use the function nsort_by in the module List::SomeUtils.

use strict;
use warnings;
use List::SomeUtils qw(nsort_by);

my @list = ( '1,cat', '2,dog', '22,mouse', '11,eel', '001,elk', '13,mi
+nk'); 

my @sorted = nsort_by {/0*(\d+)\,/;$1} @list;

{local $" = q(', '); print qq('@sorted'\n);}
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OUTPUT:

'1,cat', '001,elk', '2,dog', '11,eel', '13,mink', '22,mouse'