You should:

%menu_values = ('eenie'=>'one', 'meenie'=>'two', 'minie'=>'three');
print $CGI->popup_menu(-name=>'menu_name', -values=>\%menu_values);
[download]

The {a => 1} syntax makes a hash reference (anonymously). The \%menu_values makes a reference to the named hash %menu_values. See also perldata for more about hashes, and perlreftut and perlref for more about references.