The decision comes after the death of Andrew Coffey, a Pi Kappa Phi pledge who was found unresponsive after a party.
Moreno ordered an autopsy on Ellis's body. The police in San Marcos, Tex., where the university is, said at a news conference on Tuesday that alcohol may have been a factor, but that the cause of death would not be confirmed until toxicology results are available, which could take up to two months.
Greek life is suspended at Texas State. He was staying at the off-campus apartment complex with four other fraternity members.
The death of Matt Ellis, a business sophomore transfer student from Humble, Texas is under investigation. They also said they have had no previous knowledge of alcohol-related incidents with the fraternity.
Some students said tighter rules regarding fraternities and sororities are long overdue as they have gone largely unregulated in the past.
Ellis's friends told authorities that Ellis had attended an off-campus social event Sunday with members of his Fraternity.
Texas State's Greek organizations must register all social events through the Greek Affairs Office.
Texas state isn't the only school cracking down on fraternities and sororities. No arrests have been made at this time.
Texas State University has suspended all Greek life on campus after a student was found unresponsive the morning after attending a fraternity event, the university's president said in a statement.
San Marcos Police said Matthew Ellis was a pledge at Phi Kappa Psi and police believe alcohol may have contributed to his death. EMS personnel were not able to revive him and he was pronounced dead.
It is imperative that our entire university community develop a culture that places the highest priority on the safety of its students, faculty, and staff.