A 31-year-old man had been arrested on suspicion of murder, police said, adding that they were also investigating the incident involving the van that they believed was linked.
Police were called just after 4:00 am (0300 GMT) after two people were found dead in the street. The body of a man was also found at another location.
The three people involved in the van incident were being treated in hospital, a police statement said.
Local resident Glen Gretton said he was woken up at around 5:00 am by the sound of a series of police cars passing his home.
“I heard a police car go past. It was driving extremely quickly, followed by another one, another one, the 46-year-old delivery driver said.
“They just kept coming so I knew something quite major… was happening somewhere around the city centre,” he said.
“This is an horrific and tragic incident which has claimed the lives of three people,” Chief Constable Kate Meynell said.
“We believe these three incidents are all linked and we have a man in custody,” she added.
Television footage of Nottingham showed the centre of the city cordoned off, with a heavy police presence.
