The suspect, identified by LAPD as 35-year-old Ashkan Amirsoleymani, was arrested and booked for three counts of attempted murder.
He was wheeled out of the scene on a gurney with what appeared to be self-inflicted wounds.
The three medical worker victims were taken to nearby trauma centers for treatment.
The weapon used was a 3-to-4-inch knife recovered by police, officials said.
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"The whole family, we love her, she's part of our family. And I really hope that she's doing good and that she will be OK," said Pat Koren, a friend of one of the victims. "She came to work today to save lives, not to get stabbed."
Police say that they are familiar with the man responsible for the attack.
Amirsoleymani has prior charges for assaulting an officer and resisting arrest, according to investigators. His motive in Friday's incident is unclear.
Two of the three victims have been treated and released, while the third is in stable, but fair condition.
Amirsoleymani's bail is set at $3 million dollars.