At least 40 cyclists were injured, with most suffering cuts and broken bones, but nobody was killed, authorities said.
Police said the suspect, whose name they did not release, fled the scene of the incident Friday evening in Porto Alegre. He was brought in for questioning Monday after authorities found his abandoned car over the weekend.
The man claimed riders surrounded his vehicle and began beating on it, causing him to panic and fear for his life, police said.
But the lead investigator in the case called that version of events "fanciful," without giving other details.
Inspector Gilberto Montenegro told Globo TV network's G1 website that the man could face charges of attempted homicide. Under Brazilian law, prosecutors can decide whether to bring charges only after police close their investigation, which may take 30 days. The man is currently free.
Montenegro also said the number of people hit and injured rose to 40. Previously, police said 16 people were hurt.
Cyclists in the Critical Mass ride told the Folha de S. Paulo newspaper that no riders were threatening the motorist.
"He drove behind us for two blocks, and people were trying to stay calm. Then in the third block he ... floored it on top of everyone," Marcelo Guidoux Kalil told Folha. "It was a scene of war, with twisted bicycles and people bleeding on the ground."
In the video, thuds and sharp sounds of metal on metal are heard as the car accelerates directly through the pack of cyclists.
Scores of riders and eyewitnesses screamed and asked bystanders to call police and ambulances as they began administering first aid to the victims.