The 24-year-old died at the hospital. The other man, aged 30, is in a stable condition.
The alleged attacker was asked to leave the centre “only and solely in relation to a domestic incident” unrelated to the church that occurred on Wednesday.
It’s thought the 16-year-old had a family member who attended the centre and was at the facility on Thursday.
Det Chief Insp Jones said the assailant was of “Asian descent”.
A young Scientologist, who asked not to be identified, told AAP his mother was inside the facility and he’d been stopped from entering to see her.
“I came down when the first (media) camera crew showed up but I was told it wasn’t a huge deal,” he told AAP. He was not initially aware two people had been stabbed.
“It’s a huge building, a lot of people come from around Asia to study here,” he said.
“It offers a lot of services other (Scientology properties) don’t.”
The church on its website says the “Ideal Advanced Organisation in Sydney provides advanced religious services to Scientologists from across Australia, New Zealand and the Asia Pacific region”.
The massive 13,500 square metre building – which was opened in September 2016 – is the largest Scientology centre outside the United States.
The site formerly housed the National Acoustic Laboratory and was purchased by the church for a reported $37 million in 2014.