Robert Nicholson, 36, was on his way to work when he saw the chaotic scene play out.
Nicholson, who works in digital marketing, said the car ran into the group of cyclists "head on." He said the driver "made no attempt to slow down as he hit the cyclists."
"There was a bike flying into the air," he added. "I would say it was deliberate."
Another witness, Ewelina Ochab, said she saw the car driving at a high speed.
"I heard some noise and someone screamed, I turned around and I saw a silver car driving from the crossing, very fast and close to the railings," she told Euronews.
"There was a loud bang from the collision and a bit of smoke," said Ochab, who works as a legal researcher and human rights advocate. "The driver did not get out. The guards started screaming to people to move away."
Jason Williams, 45, told NBC News he saw the car "driving really fast" before it "screeched" and hit the barriers.
Earlier, he told "Good Morning Britain" that police told passersby to "get out of the area."
The crash occurred at 7:37 a.m. local time (2:37 a.m. ET).
In a statement, London Mayor Sadiq Khan said: "All Londoners, like me, utterly condemn all acts of terrorism on our city."
Prime Minister Theresa May added on Twitter: "My thoughts are with those injured in the incident in Westminster and my thanks to the emergency services for their immediate and courageous response."
Last year's terrorist incident saw a man drive his car across Westminster Bridge and stab a police officer to death. Five people were killed, including the officer, and more than 50 injured.