The Oakland Police Department says the fire is still under investigation.
There was speculation that it was related to protests against Yudof over massive budget cuts to the University of California system.
When firefighters got to the Volkswagen at 2 a.m. it was fully engulfed in flames. The Alameda County bomb squad was called out, but no bomb was found. The fire did not spread and caused no other damage, but it did have police concerned.
"The vehicle is located near a prominent member of the University of California faculty or staff and that caused some concern and so more officers came out to investigate this suspicious car fire," said Oakland Police Sgt. Barry Donelan.
The burning car was parked on Woodmont in the Grizzly Peak Estates.
"I smelled something burning, and I was curious and I went around the building, and I saw a car completely burned down," said contractor Bruce Nooraei.
UC police have heightened security for Yudof because of recent threats against him, and also protests in front of his home last month. Protestors are upset about recent budget cuts, tuition hikes and employee furloughs. Oakland police say the car belongs to a neighbor of Yudoff's.
"Given the fact that it's the middle of the night, a fire takes place in a car near his residence, he's had threats in the past -- it's certainly a concern for the police department, and we're going to investigate it to the best of our ability to figure out what's going on here," said Sgt. Barry Donelan.
Later in the morning, President Yudof left his home headed to Sacramento for an event. He wouldn't stop to talk about the situation; neither would his wife, who left shortly after him. But the UC office of the president says the Yudof's extend their thanks to the firefighters and police who helped in this investigation.