Shoe is pronounced ʃuː. So what’s odd about that? Well, no other word that I can think of that ends in <oe> has the vowel uː. Most of them have əʊ, as in:
doe floe foe hoe roe sloe toe woe
The two names Chloe and Zoe (sometimes written Chloë and Zoë) are pronounced ˈkləʊi and ˈzəʊi.
Thanks to Petr Rösel for the addition of canoe = kəˈnuː.