Police said they were initially called to Ilkeston Road, where two people were found dead in the street.
Officers were then called to another incident on Milton Street, where a van had attempted to run over three people. They are currently being treated in the hospital.
A man was also found dead on Magdala Road.
Police declared a "major incident" in the city, and said they arrested a 31-year-old man on suspicion of murder and that he remains in police custody.
Chief Constable Kate Meynell said: "This is an horrific and tragic incident which has claimed the lives of three people. We believe these three incidents are all linked and we have a man in custody. This investigation is at its early stages and a team of detectives is working to establish exactly what has happened."
Nottingham police said a number of roads in the city will remain closed as the investigation progresses.
Prime Minister Rishi Sunak has thanked police and emergency services for their continuing response to what is happening in Nottingham.
"I am being kept updated on developments," he said, adding: “The police must be given the time to undertake their work. My thoughts are with those injured, and the family and loved ones of those who have lost their lives."
Home Secretary Suella Braverman tweeted that she is "shocked and saddened that three people have lost their lives" in Nottingham.
“My thoughts are with those affected by this incident. I have spoken to Nottingham Police Chief Constable and I am receiving regular updates. I am thankful to the emergency services for their response.”
Nottingham City Council leader David Mellen said: “I am shocked and saddened by these horrific deaths. My thoughts and prayers are with those who knew and loved the three people who have died and those who have been injured, and to the communities where they lived."
Mellen also said he is grateful to the police for swiftly making an arrest and for all the emergency services responding to "this tragic situation."