A spokeswoman for Unite said it was alerted to a burst pipe at its The Plaza site, in Claypit Lane, in the early hours of the morning today (Wednesday).
Students were evacuated from flooded areas of the building while alternative accommodation is being organised.
One Twitter user posted on the social media site at about 4.30am, after she said she had a "terrifying" wake up call to find flooding inside a flat at The Plaza.
Other people have also posted on Twitter about the flooding, including one who said the flooding had reached the eighth floor.
A spokeswoman for Unite, which runs the student block, said: “In the early hours of this morning we were alerted to a burst pipe at our Plaza property in Leeds, which has affected some areas of the building.
"We have evacuated the flooded areas and colleagues are looking after those students while we arrange alternative accommodation.
"We are working closely with our university partners and are working to resolve this issue as quickly as possible.”