Yes, regular expressions can interpolate variables into them:

my $string_to_find = 'hidden';
my @array_to_search = qw(Foo whathiddenever Bar 12hidden456);

say "Found $_" for grep {m/\Q$string_to_find/} @array_to_search;
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You may also decide you don't need a pattern match, and if you can come to that conclusion you avoid the problem of treating strings as code:

say "Found $_" for grep {index($_, $string_to_find) > -1} @array_to_se
+arch;
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You can observe the rules of how interpolation works in regular expressions by reading perlop and perlre. The index function is also documented at perldoc -f index.

An advantage of the index approach is that you're not exposing the regular expression mini-language and engine to arbitrary strings, which could contain code. It's also lighter-weight, not invoking the engine.