The 51-year-old was also arrested on suspicion of dangerous driving, officers said, and he remains in police custody.
Videos circulating on social media during the protest on Saturday in Fisher Gate in the centre of Nottingham appear to show a car being driven through crowds of protesters on the streets.
Although the details of the incident have not been confirmed by police, a man suffered leg injuries as a result.
Assistant Chief Constable Gerard Milano, of Nottinghamshire Police, said on Sunday: “We’ve arrested a man as part of a live investigation into an incident that happened in Fisher Gate at around 3pm yesterday.
"As a result of our ongoing enquiries, we are questioning a 51-year-old man on suspicion of causing grievous bodily harm and dangerous driving. He remains in police custody."
The incident took place during large demonstrations in Nottingham city centre throughout Saturday afternoon.
Protests were held both against the Police, Crime, Sentencing and Courts Bill, which many activists argue will limit freedoms to hold demonstrations, and in support of Palestine.
Hundreds of locals descended into the city centre, waving flags and placards, to protest Israel’s continued bombardment of Gaza, which began in response to the militant group Hamas firing rockets over the border at Israeli towns.