The suspect, who has also been taken to hospital, was Tasered and arrested, Scotland Yard says.
Two police officers have been taken to hospital after being stabbed in central London, the Metropolitan Police says.
The incident, which took place near Leicester Square at about 06:00 BST, is not thought to be terror-related.
The condition of the officers is not known.
A Taser was used, Scotland Yard says, and a man was arrested on suspicion of grievous bodily harm and assaulting an emergency worker. He is also being treated in hospital.
London mayor Sadiq Khan branded the attack “utterly appalling”.
He said: “These brave officers were doing their duty and assisting the public at this momentous time for our country.
“My thoughts and prayers are with them, their loved ones and police colleagues following this disgraceful attack.”