The event was due to take place on April 30 and May 1 but logistical problems mean the velodrome will not be ready until at least May 31.
"The track cycling test event has been cancelled and will be replaced by a training opportunity June 25th through the 27th,” Mario Andrada told reporters.
"We are 120 per cent confident it will be ready for the Olympics."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Andrada said the delay came in laying the track, which is made from Siberian wood.
"We had some logistical problems, such as unloading the wood into the venue and to install containers and offices, and we realised that it was too close for us to make sure that the track was perfectly installed," Andrada said.
South America's first Olympic Games begin on Aug. 5 and run until Aug 21.
(Reporting by Bradley Brooks, writing by Andrew Downie, editing by Ed Osmond)
