The fire broke out in the engine of the vehicle which had been parked outside Orchard Veterinary Centre in Holyhead Road at 11.03am.
Crews from West Bromwich attended.
West Bromwich fires station watch commander Jason Jew said: "The driver was coming down the road and the van conked out.
"He tried to start it a couple of times, managed to get it onto the vet's forecourt, and when he was on the phone it caught fire."
He said he believed the cause was due to electrical fault in the engine.