Two men and two women have been injured following the incident in De Montfort Street shortly after 12.30am.
The incident happened following a report of a fight at the same location, Leicestershire Police said.
Three of those hurt are in hospital with serious injuries, while one man had minor injuries.
Police have said it is understood that the suspect and the four victims involved in the collision had all been in attendance at a private event nearby prior to the collision.
A 31-year-old man, from Leicester, has been arrested on suspicion of causing grievous bodily harm with intent and causing serious injury by dangerous driving following the collision.
He remains in police custody where he is being questioned by detectives.
The car believed to have been involved in the incident has been found in nearby Margaret Street and has been recovered as part of the investigation.
Detective Inspector Jenny Tattersall said: “We understand the serious concern there will be about this incident.
“Four people currently remain in hospital and an investigation is ongoing as we continue to establish the full circumstances and the events leading up to this incident. A man remains in police custody and will be questioned by officers.
“A large cordon is in place in the area of De Montfort Street and will remain while enquiries, including forensic investigations, are carried out.
“We do ask that people do not speculate about this incident, including on social media, in order to allow a thorough investigation to take place.
“We have officers at the scene carrying out enquiries and providing reassurance. Please do speak with them regarding any information you may have or any concerns you may have.
“You can also contact police on 101, quoting incident number 27 of 31 May.”
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