The 31-Balboa bus was near Market and Main streets around 10:30 a.m. when the accident occurred, authorities said.
A rope connecting to the overhead poles on the bus came loose and struck a nearby bus stop sign, Muni spokesman Paul Rose said.
The sign hit an adult leading a group of schoolchildren on a field trip and also hit one of the children, fire spokeswoman Mindy Talmadge said.
Those two both fell onto another adult and child. All four suffered minor injuries and were taken to a hospital as a precaution, Talmadge said.
The incident delayed Muni service, including the F-Market & Wharves streetcar line, for about 30 minutes, Rose said.