The car struck the woman around 10:30 a.m. Saturday morning at the intersection of Broadway and Mason in San Francisco.
Muni says it is now investigating the incident but does not believe driver error or equipment problems were involved.
Witnesses say they tried unsuccessfully to warn the woman.
"I saw the brakeman hit the brake and everyone yelled 'look out, look out!'" an eyewitness told ABC7 News. "They hit the brake again and that was it."
The woman's injuries are not known at this time.
The grip man has been put on a non-driving status while he is being tested for drug and alcohol use, which is standard procedure after an accident.