Assuming eventually your input will be a file with multiple modules, you could parse it into a more complex data structure (array of module data, where each module is represented as a hash):

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

my @modules;
while(<DATA>){
    push @modules, { name => $1 } if /^module (\w+) \(.*\)/;
    $modules[ -1 ]->{ input }  = [ split /,/, $1 ]   if /^input (.*);/
+;
    $modules[ -1 ]->{ output } = [ split /,/, $1 ]   if /^output (.*);
+/;
    $modules[ -1 ]->{ wire }   = [ split /,/, $1 ]   if /^wire (.*);/;
    next if /^endmodule/;
    if( /^(nand|nor|other)/ ) {
        push @{ $modules[ -1 ]->{ gates } }, {};
        @{ $modules[ -1 ]->{ gates }[-1] }{ qw( type name output input
+_A input_B) } = split /[\s\(\),;]+/;
    }
}
print Dumper \@modules;

__DATA__
module circuit_17 (N1,N2,N3,N6,N7,N22,N23);
input N1,N2,N3,N6,N7;
output N22,N23;
wire N10,N11,N16,N19;
nand nand2_1 (N10,N1,N3);
nand nand2_2 (N11,N3,N6);
nand nand2_3 (N16,N11,N2);
nand nand2_4 (N19,N11,N7);
nand nand2_5 (N22,N10,N16);
nand nand2_6 (N23,N16,N19);
endmodule
[download]

resulting in

$VAR1 = [
          {
            'input' => [
                         'N1',
                         'N2',
                         'N3',
                         'N6',
                         'N7'
                       ],
            'gates' => [
                         {
                           'input_A' => 'N1',
                           'name' => 'nand2_1',
                           'type' => 'nand',
                           'input_B' => 'N3',
                           'output' => 'N10'
                         },
                         {
                           'input_A' => 'N3',
                           'name' => 'nand2_2',
                           'type' => 'nand',
                           'input_B' => 'N6',
                           'output' => 'N11'
                         },
                         {
                           'input_A' => 'N11',
                           'name' => 'nand2_3',
                           'type' => 'nand',
                           'input_B' => 'N2',
                           'output' => 'N16'
                         },
                         {
                           'input_A' => 'N11',
                           'name' => 'nand2_4',
                           'type' => 'nand',
                           'input_B' => 'N7',
                           'output' => 'N19'
                         },
                         {
                           'input_A' => 'N10',
                           'name' => 'nand2_5',
                           'type' => 'nand',
                           'input_B' => 'N16',
                           'output' => 'N22'
                         },
                         {
                           'input_A' => 'N16',
                           'name' => 'nand2_6',
                           'type' => 'nand',
                           'input_B' => 'N19',
                           'output' => 'N23'
                         }
                       ],
            'name' => 'circuit_17',
            'wire' => [
                        'N10',
                        'N11',
                        'N16',
                        'N19'
                      ],
            'output' => [
                          'N22',
                          'N23'
                        ]
          }
        ];
[download]