I don't want the hash entries where single digit numbers are keys

You can delete a hash slice:

delete @hash{0..9};
[download]

Note that because your question isn't directly related to the OP, and the OP is ~13 years old, it would have been better if this was posted as a new question, which is why I've considered your node. Update: Node has since been reparented, and I added link to the original parent node.

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

my $hash = {
         'abc' => {
                 def => 1,
                 ghi => 2,
                 jkl => 3,
                },
        'mno' => {
                 pqr => 4,
                 stu => 3,
                 vwx => 5,
                },
         2   => {
                 def => 5,
                 stu => 2,
                },
         0   => {
                 def => 3,
                 stu => 1,
                },                
};

print Dumper $hash;

for my $key (keys %$hash) {
    delete $$hash{$key} if $key =~ /^\d+$/
}

print Dumper $hash;
[download]

$ perl delete_hash.pl
$VAR1 = {
          'mno' => {
                     'pqr' => 4,
                     'vwx' => 5,
                     'stu' => 3
                   },
          '0' => {
                   'def' => 3,
                   'stu' => 1
                 },
          'abc' => {
                     'def' => 1,
                     'jkl' => 3,
                     'ghi' => 2
                   },
          '2' => {
                   'def' => 5,
                   'stu' => 2
                 }
        };
$VAR1 = {
          'mno' => {
                     'pqr' => 4,
                     'vwx' => 5,
                     'stu' => 3
                   },
          'abc' => {
                     'def' => 1,
                     'jkl' => 3,
                     'ghi' => 2
                   }
        };
[download]

I like your solution. The regex could be different if OP really only wants to delete keys with single digits instead of multiple digits. I suggest using the arrow notion when using a hash reference.

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

my $hash = {
         'abc' => {
                 def => 1,
                 ghi => 2,
                 jkl => 3,
                },
        'mno' => {
                 pqr => 4,
                 stu => 3,
                 vwx => 5,
                },
         2   => {
                 def => 5,
                 stu => 2,
                },
         0   => {
                 def => 3,
                 stu => 1,
                }, 
         123 => {
                 xyzzy => "and nothing happens"
                },
};

#print Dumper $hash;

for my $key (keys %$hash) {
    delete $hash->{$key} if $key =~ /^\d$/
}

print Dumper $hash;

__END__
$VAR1 = {
          '123' => {
                     'xyzzy' => 'and nothing happens'
                   },
          'abc' => {
                     'def' => 1,
                     'jkl' => 3,
                     'ghi' => 2
                   },
          'mno' => {
                     'stu' => 3,
                     'pqr' => 4,
                     'vwx' => 5
                   }
        };
[download]

I suggest using the arrow notion when using a hash reference.

I agree that the arrow notation tends to be clearer.

That's actually what I use most of the time, or at least what I have been using most of the time in the last four to five years, but I sometimes still use the other notation ($$hash{$key}), especially when it is very simple.

Note that braces - { abc => 123, def => 456 } - create a reference to an anonymous hash which should be assigned to a scalar, e.g. my $hash = { abc => 123, def => 456 };. If you want an actual hash use parentheses - my %hash = ( abc => 123, def => 456 ); - instead.