The prime minister retaliated by accusing Sir Keir of giving “lawyerly” answers rather than explaining the details of his own extra paid work.
Speaker Sir Lindsay Hoyle called several times for better behaviour.
Sir Keir then withdrew it, saying: “I withdraw it but he is no leader.”
The Speaker described the atmosphere at Prime Ministers Questions as “ill-tempered”.
The row between Mr Johnson and Sir Keir came during a series of exchanges over the issue of MPs’ second jobs, which has dogged Westminster for several weeks.
On Tuesday, both Labour and the Conservatives revealed their own set of proposed reforms, following Tory MP Owen Paterson breaking the rules on paid lobbying on behalf of two companies.
Sir Keir, whose party wants a ban on almost all second jobs, said Mr Johnson was “a coward, not a leader”.
But the prime minister responded that Sir Keir needed to give more details of his own work as a lawyer since becoming an MP in 2015, saying that in a “lawyerly way” he was “trying to preach to others for exactly the sorts of actions that he took himself”.
Amid raucous scenes in the chamber, Sir Lindsay told Mr Johnson not to ask questions of the Labour leader, as this was not the point of Prime Minister’s Questions.
The Speaker interrupted the prime minister’s reply to Sir Keir Starmer and told him to sit down during Prime Minister’s Questions.
Lindsay Hoyle had previously warned Boris Johnson in the same session about asking the Labour leader questions, reminding him it was his role to answer questions at the weekly event,.