Android - Limit YouTube to Wi-Fi only

Don't know of any YouTube option for that end, but if you are open to use an app to limit other apps, you can give a go to Onavo Count | Monitor Data that has an option to limit the app to Wi-Fi only:

Save money on your mobile bill - avoid costly overage fees! Onavo Count puts you in control of your 3G data plan. Easy setup, three brand new widgets, tailored alerts and automatic blocking tools will keep you safe from bloated data bills.

Update September 2016:
It looks like Onavo Count is no longer compatible with some modern Android devices including devices like Nexus 6P. Onavo has a new "Protect Free VPN+Data Manager", which still has the above functionality in addition to some cool VPN features.

avast! Mobile Security has, in addition to multiple layers of protection, a firewall module that allows individual control of each application with toggling of Wi-Fi/data/roaming access.

Onavo also works great as mentioned but doesn't have the other features that Avast has.