The boast - which police are investigating - was made by Rayhan Qadar on his Twitter account under the name of "Ray Pew".
It prompted a storm from other Twitter users, who reported the 21-year-old to police and called for him to apologise.
Despite saying the tweet was a "bad joke" and insisting he had not hit a cyclist, he was promptly sacked from his job at Hargreaves Lansdown, which sells shares and investment funds.
A spokesman for the Bristol-based company said: "One of our employees has failed to conduct themselves to the standards we expect of our staff. We find these online comments totally unacceptable. Upon becoming aware of this issue we have terminated this person's employment with immediate effect."
The tweet that has cost Rayhan Qadar his job. Photo / Screengrab
Mr Qadar's post was retweeted 152 times and helped raise his number of followers above 1300 before he made his account private and changed his description.
Greater Manchester Police wrote: "If you hit a cyclist, you are obliged to stop. I suggest you call 101 as soon as possible, I will forward the details on."
A few hours later Mr Qadar wrote: "My previous tweet about the cyclist was obviously not true. I did not hit cyclist. Not today. Not ever. A bad joke on my part it seems."
Two minutes later he added: "Sorry if anyone thought i actually hit a cyclist. Anyone who follows me on Twitter know 99% of the things I tweet is nonsense."
But the damage was done. A police spokesman said: "We are aware of a tweet regarding a collision between a cyclist and a car. We are looking into it and we're asking for witnesses to come forward."
Police are still investigating despite Mr Qadar contacting the force directly to explain that his tweet had been a joke.
The drastic consequences for the young stockbroker have prompted a new debate over whether his bosses went too far by sacking him.
One Twitter user wrote: "What I think is disgusting is the total over-reaction from the righteous Twitter Nazis over a joke tweet. It's a bad joke, end of."
And one of Mr Qadar's original critics posted: "I didn't want him sacked to be honest, it is a bit harsh. An apology would have done for me."
- Daily Mail