Nobody was injured and the two Boeing 737s were taken out of service for inspection. Passengers were being moved to other flights.
The incident occurred around 7:30 a.m.
Photographs posted online showed one plane's winglet -- the vertical tip on the main wing -- touching the horizontal stabilizer at the rear of the other plane.
John Cox, a former pilot for U.S. Airways, said the Burbank airport is known for crowding lots of planes into a small space.
"It's very tight quarters in there," said Cox, who runs Safety Operating Systems, an aviation safety firm in Washington. "You have to be careful on parking."
The ground crew is responsible for pushing planes back from the gate, he said. In addition to the driver of the towing vehicle, there is normally an observer at each wing to make sure the area is clear, he added.
"It's a fender-bender," Cox said after looking at the photographs. "That's the best way I can describe it."
Southwest said the flights were 2183 to Phoenix with 114 passengers and 4721 to Sacramento with 106 passengers.
Victor Gill, a spokesman for the airport, said the two planes had been parked at adjoining gates A-1 and A-2.
He said the airport reported the incident to the
A spokeswoman for Southwest said in an email: "We are conducting an internal review, and will work with relevant agencies, as necessary."