The incident happened before kick-off at Fat Cat Bar.
Chief Inspector Neil Williams, of Nottinghamshire Police said: “Officers were quick to attend reports of a disturbance that broke out in Chapel Bar, in the city centre, at around 12.15pm today (Sunday, 6 February ) following reports of windows being damaged.
“Three people suffered very minor injuries during the incident before the fans were quickly moved on by officers in the area.
“Police were also quickly on the scene following reports of a fight and windows being smashed in Byard Lane, in the city centre, at around 3.20pm this afternoon.
“We take any reports of violence extremely seriously and anyone found to be breaking the law and identified as being part of these incidents will be arrested and dealt with.
“We want everyone to enjoy the match but in a safe manner so we have a large number of officers out on patrol today and throughout this evening to make sure everyone can enjoy the match safely.
“We recognise the vast majority of fans are simply there for a good time and to enjoy the game but we would like to reassure the public officers will be there to monitor the fans and step in should they be needed.”
Witnesses or anyone with any information about the incidents are asked contact the police on 101, quoting incident 182 of February 6.
— Ian (@speedyred711) February 6, 2022