Transport Secretary Chris Grayling knocked a cyclist off his bike as he opened the door of his ministerial car on the street outside the Palace of Westminster.
Video footage obtained by The Guardian showed cyclist Jaiqi Liu, 35, crashing to the ground and his bike hitting a lamppost in the incident on October 12.
A spokesman for Mr Grayling said that he immediately went to check if the rider was all right and apologised to him.
He can be seen on the video bending over and putting his hand on Mr Liu's shoulder and speaking to him as he sat on the pavement where he landed. The pair then shook hands.
The Transport Secretary's car was in a stationary queue of traffic waiting for lights to change when Mr Liu's cycle passed it on the inside.
Mr Liu, who works at the World Bank, told the Guardian that he was in shock after the accident and only became aware later of pain in his back, legs and head.
He said the incident caused damage to his bike's wheel, brakes, mudguard and lights.
He said that he had informed the police in order to ensure the incident was logged, but did not expect it to be investigated. He did not recognise Mr Grayling at the time.
"It's my first and only accident and it came out of the blue," he told the newspaper.
"Definitely he should stay a bit longer to check on me. But maybe he had something more important than this to rush to."
He added: "And he says cycle lanes are the problem, which makes me angry. If he is still in the position to make cities safer for cyclists, he needs to do something."
The footage came from a camera mounted on the handlebars of another cyclist, Laurence de Hoest, who told The Guardian: "I ride into London every day and I've had a couple of close calls, so I record everything.
"This is the minister of transport and here he is swinging his door out."
He added that the incident, which occurred on a stretch of road 20 metres before a cycle lane is restored, showed that "your cycle lane is only as good as your weakest link. We need to make sure they are properly connected."
The Transport Secretary's spokesman said: "This was an unfortunate accident.
"Mr Grayling got out of the car, checked the cyclist was OK and waited until he was back on his feet. Mr Grayling spoke to the cyclist and apologised; they shook hands before he left."
Conservative MP Nadine Dorries came to Mr Grayling's defence on Twitter, saying: "The advice to cyclists re undertaking when filtering is very clear. I'm amazed that so many cyclists do that. So aware of it all along the Embankment."