This has happened quite a bit. While the QB position has been awarded Super Bowl MVP 31 times, other spots have won the award several times. Here’s the complete list of awards for other positions. (Just remember Super Bowl MVP isn't a legal bet in Virginia.)
Running back: 7
Wide receiver: 7
Linebacker: 4
Defensive end: 2
Safety: 2
Cornerback: 1
Defensive tackle: 1
Kick returner/Punt returner: 1