One of the dead could have been the shooter, said UCLA Police Chief James Herren.
Police found a suicide note and handgun, reported NBC Los Angeles, citing an unidentified source, while the LA Times said police believed a professor had been shot by someone young enough to be a student, who turned the gun on himself.
While Los Angeles Police Department spokesman Aareon Jefferson reported two fatalities from the shooting, he could not confirm any details about the victims nor provide further information about the suspect.
Bioengineering student Bahjat Alirani said police were yelling at people to run from the scene.
“I was in Boelter Hall to take a final and I exit the staircase to see SWAT-looking police yelling at everyone to evacuate immediately,” Alirani told Reuters.
“I check my email and BruinAlert had immediately sent an email to all students notifying them of a shooter in the engineering building.”
The university has more than 43,000 enrolled students.
UCLA is in the Westwood section of Los Angeles and one of the more well-regarded schools in the University of California system.
The city of Los Angeles was placed on a tactical alert citywide, which means officials can allocate resources based on need, Los Angeles Police Captain Andrew Neiman told reporters near the scene.
There were no reports of bombs or other devices, said Neiman.
Police received multiple calls of shots fired around 10am, triggering an immediate search for suspects and victims by LAPD and campus police, said officials.
Erica Roberts, a sophomore economics major from Rockville, Maryland, said she took shelter inside the student health centre about 10 minutes after she had arrived for work there.
“Everyone is really on edge and contacting loved ones to let them know we are safe,” she said.
“I’m trying to stay in contact with all my friends on campus to make sure they are OK. Everyone is just terrified.”