Two people were found dead in the street in Ilkeston Road just after 4am on Tuesday and a third man was found dead in Magdala Road, Nottinghamshire Police said.
Another three people are in hospital after someone tried to run them over in a van in Milton Street, in what police believe is a connected incident.
Police have arrested a 31-year-old man on suspicion of murder and he remains in police custody.
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Police cordoned off around 400 yards of the scene at Ilkeston Road with tape, and what appeared to be medical kit was scattered across the road.
Two forensic officers arrived and appeared to dedicate the majority of their time at a bathroom and plumbing business called Willbond.
The forensic officers eventually left the scene on foot with a black crate and large plastic bag.
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.
“We ask the public to be patient while inquiries continue. At this time, a number of roads in the city will remain closed as this investigation progresses.”
The following roads are closed while Nottinghamshire Police carry out investigations:
- Ilkeston Road
- Milton Street
- Magdala Road
- Maples Street
- Woodborough Road from junction of Magdala Road into the city
- Maid Marian Way junction of Parliament Street
The Nottingham Express Transit (NET) tram network said it has suspended all services due to “major police incidents around the city and suburbs”.
In a separate statement, NET advised travellers that NCT buses are accepting its tickets and passes, while EMR trains are also accepting its tickets and passes between Hucknall and Beeston, and Nottingham station.
Local resident Glen Gretton said he was woken up at around 5am on Tuesday morning by the sounds of a series of police cars passing his home.
The 46-year-old delivery driver, who lives in a flat in Mansfield Road in Sherwood, said: “I heard a police car go past. It was driving extremely quickly, followed by another one, another one.
“They just kept coming so I knew something quite major ... was happening somewhere around the city centre.”
Rishi Sunak said he is being kept updated on the “shocking incident” in Nottingham as police investigate, and he paid tribute to those who have lost their lives and their families.
The prime minister tweeted: “I want to thank the police and emergency services for their ongoing response to the shocking incident in Nottingham this morning.
“I am being kept updated on developments. 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.”