The truck was stolen as an employee of Creature Comfort Pet Services was dropping off a dog near Woodland Drive and East 11th Avenue.
Company owner Amy Villis says four dogs were inside the truck at the time, but two were found a few blocks away.
Two others — a reddish-brown flat-coated retriever and a spaniel-basset hound cross — are still missing.
"We've been driving around all night and going everywhere and we've had some fantastic media attention and some Facebook," she said.
"I get calls from people saying, 'I think I saw your dog.' And we've been driving here, there and everywhere. And we just can't find them. And you just fear the worst."
The truck is described as a black 2006 Ford Ranger with a red canopy.