The first attack happened at the Olive View-UCLA Medical Center in the 14400 block of Ocean View Drive in Sylmar just after 2 a.m.
According to Los Angeles County sheriff's deputies, Romiro Carnalla, 26, of Los Angeles entered the hospital, bypassed the weapons screening area, and fled into the building.
As deputies and officers searched the hospital for the suspect, they heard a woman scream. Responding officers found the on-duty nurse suffering from an unknown number of stab wounds to the upper and lower torso.
"Luckily, the deputies acted quickly and efficiently and located the suspect and prevented anyone else in the hospital to be harmed," said Deputy Juanita Navarro-Suarez.
The victim is listed in critical condition. A knife was recovered at the scene.
Carnalla was booked for assault with a deadly weapon and battery. He is being held on $55,000 bail. The motive for the attack remains unknown.
The second attack happened at Harbor-UCLA Hospital in Torrance around 9:30 a.m. Authorities identified 38-year-old Thomas Fredette of Santee as the suspect.
He entered the hospital, allegedly grabbed a nurse from behind and stabbed her in the ear with a sharp object. The victim managed to get away. She was treated for non-life-threatening injuries.
Fredette is in custody on $130,000 bail facing felony charges. He is expected in court Tuesday.