Uber driver Manuel Dias told the Sun newspaper that he was driving Cumberbatch and his wife Sophie Hunter along London's Marylebone High Street when they saw a cyclist being hit with a bottle.
He said Cumberbatch, 41, jumped out of the car and grabbed one of the attackers.
"I had hold of one lad and Benedict another," Dias was quoted as saying. "He seemed to know exactly what he was doing. He was very brave."
Tomorrow's front page: Sherlock star Benedict Cumberbatch fought off a gang of four muggers as they beat up a defenceless Deliveroo cyclist. pic.twitter.com/LYgLrI7yfV— The Sun (@TheSun) June 1, 2018
"Here was 'Sherlock Holmes' fighting off four attackers just around the corner from Baker Street," he added.
The fictional detective's home address in London is near where the attack happened.
Cumberbatch's spokeswoman declined to comment.
The newspaper didn't say when the incident occurred, but police reported that a delivery cyclist was assaulted in the street in November.
On Saturday, Deliveroo praised Cumberbatch "for his heroic actions" in a tweet.