You can either use the \Q...\E construct (documented in perlre) within a regex, or the quotemeta function call.

#\E not necessary at end of pattern
/^\Q$string/ and print "A match!\n";

#or, same thing
$string=quotemeta $string;
/^$string/ and print "A match!\n";
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update: Re-slanted my slashes. Thanks corion.