If you don't mind letting your arrays have package scope, you can use soft references like this:

use strict;
use warnings;
use Data::Dumper;

my @tablenums = ('1', '2', '3');
our (@johnData, @mikeData, @harryData);
my @any = ("any", "data", "goes", "here");

my %Tables = (
'1' => "john",
'2' => "mike",
'3' => "harry",
);

foreach (@tablenums){
    no strict 'refs';
    push @{"$Tables{$_}Data"}, @any;
}

print Dumper(\(@johnData, @mikeData, @harryData));
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Further reading: Symbolic references