The crash was reported at about 9:30 a.m. near the intersection of Powell and O'Farrell streets, San Francisco Officer Albie Esparza said.
A vehicle rear-ended the cable car, which was not damaged in the crash, Muni spokesman Paul Rose said.
No one was injured in the crash.
Cable car service was disrupted due to the crash and was still affected as of 12:45 p.m., Rose said. Bus shuttles are taking passengers around the intersection while the investigation is ongoing, he said.
Police suspect the driver of the vehicle may have been under the influence of alcohol or drugs because he refused to get out of the vehicle and make contact with the cable car operator, Esparza said.
The driver had a passenger give his information to the operator and then the vehicle left the scene, he said.
Police will not be able to investigate the possibility that the driver was drunk since the vehicle left before police arrived at the scene, and since information was exchanged, the crash is not being investigated as a hit-and-run, Esparza said.