The Los Angeles Times website identified the suspect as Layla Rosetta Trawick, 35, of Antioch, and said she was carrying two bloody knives when she was taken into custody.
Paramedics sent to the 7100 block of Santa Monica Boulevard at 12:48 p.m. transported one person in critical condition and another with less serious injuries to a hospital, said Inspector Frederic Stowers of the county fire department.
Sgt. Josh Mankini of the sheriff's West Hollywood Station said the stabbings occurred on the second floor of the building.
The deputy was in the store when he heard screaming, saw the suspect, identified himself as a law enforcement officer and arrested her at gunpoint, Mankini said.
"Talking from the victims, it appears the stabbings were random," the sergeant said. "That has not been confirmed yet, however."
Numerous people in the store called 911, thinking a man with a gun was involved in a crime, but that was not the case, Mankini said.
Editorial note: An earlier version of this story said five people were stabbed. The correct number is four.