She remained in custody Wednesday afternoon, it said, noting officers had seized a pair of scissors at the scene.
The four victims -- aged 34, 39, 42, and 52 -- were taken to hospital where two remained with injuries not "believed to be life-threatening or life changing," the force added. The two other men attacked were discharged within hours.
"While still at an early stage of the investigation, we would like to reassure the community that we currently believe this to be an isolated mental health related incident," Met Chief Superintendent Jason Stewart said in a brief statement.
Witnesses working in a nearby restaurant said police had used tasers to arrest the woman, who was known locally as a homeless person who regularly frequented the area.
"They (police officers) were chasing away the lady who had a knife in her hand," waiter Ahmad -- who declined to give his surname -- told AFP.
"I saw the lady get tased (tasered) by the police, it was the only way they could get her to drop the knife."
Police did not confirm the use of tasers in their statements.
The Covent Garden street where the incident unfolded, lined with stores and outdoor seating, was cordoned off with police tape for several hours.
Striking images published by media showed an air ambulance helicopter in nearby Trafalgar Square.
Another witness, waiter Arjan, said staff saw the confused aftermath of the stabbings, noting "even the victims, they didn't believe what was happening".
"We saw people lying down and the police arrived immediately," he said.
"We know the lady. I don't know her name but she is always on this street, she was homeless and never wore shoes."
