The stabbing near Leicester Square at 06:00 BST is not related to the Queen’s death or terror-related, police say.
Mayor of London Sadiq Khan branded the incident “utterly appalling” at a “momentous time for our country”.
A man in his 20s has been arrested on suspicion of grievous bodily harm and assaulting an emergency worker.
The officers’ families have been told about the “very concerning” attack, Scotland Yard said.
Praising the officers’ bravery, Sir Mark said: “It’s a reminder to me that with all the calls for reforming the Metropolitan Police, which are absolutely necessary, we should never forget that we’ve got thousands of dedicated men and women going out every day who are prepared to be brave for Londoners.”
The stabbing took place close to Haymarket, between Leicester Square and Piccadilly Circus, which is home to many of London’s theatres and Chinatown.
Leicester Square, an area usually bustling with commuters and tourists, is almost completely inaccessible to the public.
Police lines stretch from Haymarket south to Leicester Place, with the northern half of the square completely shut off.
Several police officers are patrolling the cordon, with the strongest presence on Coventry Street, near the junction with Haymarket.
In the no man’s land between the police tape, there are a few police cars and vans. I also spotted an incident response vehicle left nearby.
There is a sense of confusion among those in area.
Shop owners tell me they came to work and saw the police setting up the cordon, but eyewitnesses are hard to come by as it seems the attacks happened too early for anyone to see in an area famed for its nightlife.
The deputy assistant commissioner, Stuart Cundy said the attack was not believed to be terrorist in nature or linked to the events relating to the death of the Queen.
The incident came as the UK prepared for a huge security challenge in the lead-up to the Queen’s funeral on Monday.
The London mayor, Sadiq Khan, called the attack “utterly appalling” and “disgraceful”. He said he had spoken to Rowley about the incident and remained in close contact, and he urged anyone with information to come forward.
“These brave officers were doing their duty and assisting the public at this momentous time for our country,” he said. “Attacks against the police will not be tolerated and any perpetrators will be caught and prosecuted.”
Discussing the incident on BBC News on Friday morning, Khan said a member of the public “did the right thing” and went to a police officer, “and police officers responded”.
Supt Justin Browne of the Met said: “Every day, police officers go out on the streets to keep the communities of London safe. In doing so they often have to put themselves in the way of danger, putting their own welfare at risk in order to protect others.
“The actions of these two officers, and their colleagues, exemplifies the key value of courage that runs through the core of the Metropolitan police and they will be offered all the support they need as they begin their recovery from this terrifying incident.”
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