I created the bit mask from the mask by replacing 0's by \x00 and 1's by \xff. Then, you can use bitwise & and can easily remove the resulting \x00's:

#!/usr/bin/perl
use warnings;
use strict;

my $string = join q(), map int rand 10, 1 .. 400_000;
my $mask   = join q(), map int rand 2,  1 .. 400_000;
$mask =~ tr/01/\x00\xff/;

my $result = $string & $mask;
$result =~ tr/\x00//d;
print $result;
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Updated: Using tr/ instead of s/ at line 10 speeds the method up.