The cab hit people gathered on the sidewalk outside the Stingaree nightclub at about 2 a.m., The San Diego Union-Tribune reported.
"Probably the most serious [injury] was a woman who had been pinned against the wall by the cab and her leg was amputated below the knee," San Diego Fire and Rescue spokesman Maurice Luque told NBC San Diego.
Bystanders attacked the driver after the crash. He was taken to the hospital with a broken nose, according to News 10.
Police said there was no indication the driver was drunk.
Cops said the driver, in the 40-50 age range, was traveling at about 15 mph when his cab jumped the curb.
"Even if he had been going 25 miles per hour, it would have been a different story," San Diego Police Lt. Todd Jarvis told the Union Tribune. "We were fortunate there were no fatalities in this incident with that many pedestrians on the sidewalk."
James Brennan, one of the nightclub owners, released a statement expressing sympathy for those hurt.
"Our deepest thoughts and prayers go out to the victims of this morning's tragic accident in front of Stingaree nightclub," Brennan said. "We are cooperating in every way possible with the San Diego Police Department in their investigation to determine what led to this incident."