In essence you can't do that. $test contains a Perl regular expression object and JSON doesn't have an out-of-the-box way to deal with them.

If you don't need to round trip the data, but are providing it for consumption elsewhere the allow_blessed function will suppresses the error, insert a 'null', and carry on:

use strict;
use warnings;
use JSON qw();

my $test = {regex => qr/^[\w\@\.]+$/, str => "this is a string"};
my $json = JSON->new();

$json->allow_blessed(1);
print $json->encode($test);
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Prints:

{"str":"this is a string","regex":null}
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Update: and if you do want to round trip it with another Perl script then think about using YAML instead:

use strict;
use warnings;
use YAML qw();

my $test = {regex => qr/\w+\W+(\w+)/, str => "this is a string"};
my $yamlStr = YAML::Dump($test);

print "YAML: $yamlStr\n";

my $andBack = YAML::Load ($yamlStr);
my ($secondWord) = $andBack->{str} =~ $andBack->{regex};

print "Second word is: $secondWord\n";
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Prints:

YAML: ---
regex: !!perl/regexp (?-xism:\w+\W+(\w+))
str: this is a string

Second word is: is
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