Anderson and Smith were found dead in a special needs classroom that serves the first through fourth grades, Burguan said.
San Bernardino Police Chief Jarrod Burguan says on Twitter that investigators believe "the suspect is down".
Authorities said that Anderson signed in at the school office then proceeded to the classroom.Although the shots fired were aimed at Smith, two students standing her were struck by the gunshots before Anderson turned the gun on himself.
The other student shot, only identified as a 9-year-old boy, was in stable condition Monday afternoon.
France migrants: Huge fire guts Grande-Synthe Dunkirk camp
The fierce blaze destroyed most of the 300 huts in the camp and had still not been extinguished at 2:00 am Tuesday (0000 GMT). Residents and local officials reported that the fire had been started after fights between Kurdish and Afghan nationals.
"We believe this to be a murder-suicide", San Bernardino Police Chief Jarrod Burguan tweeted.
"I see one of my boys, but not the smallest one", he said tearfully. "They know exactly what to do and what they need to do to keep students safe", Said Garcia to KTLA. "The victim was his wife the teacher, Karen Elaine Anderson, 53". "The children we do not believe were targeted", said police Capt.
Frantic parents running up a sidewalk looking for information about their children were not able to learn immediately what happened.
One of two students injured in the murder-suicide later died at a hospital, Burguan said.
Mayor Carey Davis said he had spoken about the shooting to White House officials about Tuesday's (AEDT) school shooting.
China's Xi meets Trump, urges trade cooperation
Last week, the president predicted in a tweet that his meeting with Xi would be "very difficult". By launching the strike while Xi is in town, Trump may have added an another item to the list.
Monday's shooting was the latest tragedy for a city that has struggled in recent years with more than its share of them.
Authorities locked down the school - which will be closed for at least two days - and students were safely escorted to Cal State University where they united with parents, reports ABC7. Aerial television footage from the scene showed students walking single-file across the campus from the school building.
"This is a tragic incident that has befallen our city", San Bernardino Police Lt. Michael Madden told reporters earlier.
An eight-year-old boy died when a gunman opened fire in a San Bernardino elementary school Monday morning.
Marina Ramos told KABC that she rushed to the school to try to pick up her grandson.
Death toll climbs in San Bernardino elementary school shooting
San Bernardino police and fire officials at North Park Elementary School on April 10, 2017 following shooting on campus. Two students were also injured during the shooting, and have been taken to a local area hospital.
The elementary school is located at 5378 N. H St.