The blaze broke out in the first-floor flat of a two-storey building in Fairlisle Close, Clifton, at around 3.17am on Sunday.
A woman, thought to be in her thirties, and two children, aged three and one, were treated at the scene for smoke inhalation before being taken to the Queen’s Medical Centre in Nottingham.
The two children were pronounced dead at the hospital, Nottinghamshire Police said, while the woman remains in a critical condition.
The man from the Clifton area was arrested on Sunday evening on suspicion of murder and attempted murder, detectives said. He remained in custody for questioning overnight.
The fire was extinguished at around 4am. Neighbouring buildings were temporarily evacuated during the incident.
A local resident, who asked not to be named, was alerted by a fire engine’s lights while watching a film, and then saw smoke billowing from the rear windows of the first-floor flat.
He told reporters: “I saw the blue lights and smoke was coming out of the top windows.”
The eyewitness said the older child was brought out of the property first, with the one-year-old being carried out by a single firefighter shortly afterwards.
Estimating that CPR was then carried out at the scene for around 20 minutes, the man added: “It was dark and raining and with the smoke I couldn’t see what was happening behind the fire engine.
“It’s sickening. I feel so sorry for the family. How is she going to feel when she finds out she’s lost the children?”