Aside from the syntax error at %hash{"my_function"} that should work:

#!perl -w
use strict;

sub my_func {
    print @_;
}

my %hash = (
"my_function" => \&my_func
);

my $func_ref = $hash{"my_function"};

&$func_ref("bla");
[download]

but I prefer to do $func_ref->("bla")

Had you posted a working code snipped, chances are you'd have found out for yourself ;-)