Use the e-modifier:

#!/usr/bin/perl
my %variables = ('$x' => 1);
my $test = '$x $y';

$test =~ s/(\$\w+)/exists $variables{$1} ? $variables{$1} : $1/e;

print $test, "\n";
__END__
1 $y
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Update: Every possible value is substituted (albeit by itself, if not existing as hash-key), if this is too much or discomforting, just split match and substitution...