Officers responded to Kaiser Permanente Medical Center in Hayward after three people showed up at the hospital at about 6 p.m. with stab wounds to their torsos, police said.
Investigators determined that the victims, two adults and a juvenile, had been stabbed in the area of 10th and G streets in Union City's Decoto District about 15 minutes before arriving at the hospital.
Their wounds were not believed to be life-threatening.
No arrests have been made in the case. Police are looking for a man in his 20s as a person of interest.
Anyone with information is asked to contact Union City police Detectives Steve Cesaretti or Roberta Paul at (510) 471-1365.