Generic version:

use strict;
use warnings;
use DBI;

my $dbh = DBI->connect(...);
my @tables = $dbh->tables(undef, undef, undef, 'TABLE');

print "$_\n" for @tables;
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The tables method should work for all databases supported by DBI. Sending a show tables query is MySQL-specific - I know it doesn't work with SQLite databases and, from long-gone memory, I'm pretty sure PostgreSQL wouldn't like it either. Any other database engine, I can only say "seems unlikely".