They say the leaks are minor and the track, which made of Siberian pine, has not been damaged. Officials say competition will continue as planned.
A spokeswoman says water came through three places above the centre of the arena. At times Sunday morning, there was heavy rain in London. The spokeswoman says repairs should be completed overnight.
The velodrome is nicknamed the Pringle because of its potato-chip shape. It has a curved roof, lowest in the centre, that captures rain to feed a tank. The rainwater can be used for watering the grounds around the building.
The venue holds 6,000 people and $147 million to build.