West Yorkshire Police confirmed that they had been notified by West Yorkshire Fire and Rescue Service that fire crews were dealing with a suspected chemical leak but were not in attendance themselves.
A University of Leeds spokesman said that the incident was "minor" but required investigation for safety reasons.
The spokesman said: "The Edge remained closed this morning [SUNDAY 12 JAN] after staff discovered an issue in the swimming pool plant room which required investigation to ensure safe operation.
“All users and staff are safe, the issue turned out to be a minor one and specialist engineers are on-site fixing the problem.
“We apologise for any inconvenience caused.
“All other facilities will reopen at 2.30pm, although the swimming pool will remain closed for the rest of the day, reopening as usual at 6.30am tomorrow.
“Please check our Facebook and Twitter channels for any further updates.”
The sports complex on Willow Terrace Road is operated by the University of Leeds and open to both students and the general public.
The Edge has an eight-lane 25m pool which is used by elite athletes. Olympic triathletes Alistair and Jonny Brownlee train there. There is also a swim school for children and adults.
The sports centre also has a gym, squash and badminton courts and offers netball, football and table tennis.