There's More Than One Way To Do It: If you need to do a lot of lookups, then grep will quickly become inefficient, and instead it will likely be worth it to build a reverse lookup table (assuming it fits comfortably into memory). With the following, you can simply write $colors{green}, $colors{red}, etc.

use warnings;
use strict;

my %fruit = (
        apple => ['red','green'],
        kiwi => 'green',
        banana => 'yellow',
    );

my %colors;
for my $f (keys %fruit) {
    for my $c ( ref $fruit{$f} ? @{ $fruit{$f} } : $fruit{$f} ) {
        push @{ $colors{$c} }, $f;
    }
}

use Data::Dump;
dd \%colors;
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By the way, always Use strict and warnings!