Does one's private parts have to be covered when making wudhu?

It is compulsory to cover one?s private parts at all times except when there is a need to expose one?s private parts, for example, answering the call of nature, etc.

There is no reason to expose one?s private parts during Wudhu. However, concealing the private parts during Wudhu is not a pre-requisite for the validity of the Wudhu. The Wudhu will be valid even though the private parts are not concealed.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai