This may be what you're after:

use strict;
use warnings;

my @array = ( "file1:aa" , "file2:bb" , "file3:cc" );

my( @found ) = grep { $array[$_] =~ m/aa/ } 0 .. $#array;
print "Matched in $array[$_]\n" foreach @found;
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Update
I wanted to point out that the difference between my implementation, and McDarren's is that his caches the elements from @array that matched, and mine caches the indices of the elements from @array that matched. It's up to you to decide which is better for you. There are subtle advantages to each.