The crash that sandwiched a car between the two Muni vehicles was reported around 12:20 p.m. on Market Street near First Street, San Francisco fire spokeswoman Mindy Talmadge said.
Three people were taken to the hospital for minor injuries, while six others declined further medical attention, Talmadge said.
Muni officials said the F-Market and Wharves streetcar line is blocked at Market and First streets. The 38-Geary and 71-Haight-Noriega bus lines are being rerouted around the intersection.
San Francisco emergency officials said most lanes near Market and First streets are blocked and advised drivers to avoid the area.