A bomb squad has destroyed the backpack and several police cars are at the scene as the 237.5km Race continues.
Chris Froome and three other Team GB riders are taking part in the race.
A Rio 2016 spokesman confirmed: "The security services found a suspicious package close to the cycle road race finish line in Copacabana and as a precaution decided to perform a controlled explosion. There is no impact to the race, which is ongoing."
Sky News' Paul Kelso said he heard a "very loud bang" from behind a grandstand.
One theory is the bag belonged to a homeless man.
The incident comes on what has been a shambolic opening day of the Olympics proper, with spectators queuing for hours and some missing events all together.
Several events were played out in front of eerily empty stands.
"We apologise for everybody standing in line outside the venues," Games spokesman Mario Andrada told reporters.
"We need to upgrade that part of the Games. We moved people from Rio 2016 (organisation) to speed up the mag and bag (security checks) and within the next hours we will be in much better shape."
There have also been reports of a military bullet coming through the roof of the equestrian centre. It reportedly landed at the feet of a photographer.