Police were called on Friday evening by Honeycutt's mother after he was behaving "erratically".
The LAPD did not identify the man involved in the standoff.
Police spoke with the suspect, a man in his 20s, face-to-face and through a cellphone before he fired at them from inside the building, officials said.
Rubenstein added that "no officers were injured and it was unknown if the suspect had been struck by the officer's gunfire".
Crisis negotiators and the SWAT team were deployed to the scene and several residences were evacuated in the area as a precaution, according to ESPN.
Honeycutt was named to the All-Pac 10 first team as a sophomore at UCLA then declared for the 2011 draft.
At 2:30 a.m. Saturday, SWAT team members were able to enter the apartment and found Honeycutt unresponsive, Sgt. Hector Guzman said.
Basketball player Tyler Honeycutt has died after a shootout with U.S. police, local media report.
Honeycutt, 27, allegedly opened fire at officers and barricaded himself inside the residence Friday night.
Honeycutt had played with UCLA from 2009-11. The suspect appears to have sustained injures consistent with a self-inflicted gunshot wound. After his second season at UCLA, he left to play in the National Basketball Association. Later that year, Honeycutt began playing for EuroLeague clubs, including BC Khimki (Russia) and Anadolu Efes Sports Club (Turkey). "Rest in peace, Tyler", it tweeted. BC Khimki expresses its deepest condolences to Tyler's family and friends...