I always thought it was a bong. It was blurred so I could be wrong, but in context it made sense.

The cigar thing brings to light some questions:

Why would VH1 blur a cigar?

Why would Prince light up a cigar of all things during a song?

Unless....it was purely a cigar wrapper, meaning he sparked up a blunt. It's obviously done for comedic effect though, so I never took it seriously.

I've read rumors (and I emphasize rumors) that Prince smoked cigarettes in the very early 80's. I've never seen pics or confirmation, so I actually find it hard to believe. However, many of us have seen him pantomime smoking a cigarette as a dance move (along with brushing his teeth and hair).