While particle mentions quotemeta, you can also use the in-line version of same. The real problem seems to be the way you are using your arrays. You're not indexing correctly. Looks like some C-style looping you've got there. How about this?

foreach my $cur_cnt (0..$#current)
{
     foreach my $base_cnt (0..$#base)
     {
           if ($base[$base_cnt] =~ /^\Q$current[$cur_cnt]\E/)
           {
                  # ...
           }
     }
}
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Better still to just iterate and forget the index unless you actually need it:

foreach my $current (@current)
{
     foreach my $base (@base)
     {
           if ($base =~ /^\Q$current\E/)
           {
                  # ...
           }
     }
}
[download]

Less is more, especially with programming.

As an explanation, the \Q starts "escaping" special characters, the \E stops, using a quotemeta equivalent.