Two children aged 1 and 3 years old, both girls, died after the fire in Fairisle Close in Clifton on Sunday 20 November.
A woman remains critical in hospital being treated for smoke inhalation.
A 31-year-old man from Clifton has been arrested on suspicion of murder and attempted murder.
Detective Chief Inspector Greg McGill, who is leading the investigation, said: “This is a deeply tragic incident and we have a large team working tirelessly to understand the full circumstances.
“Whilst we have now made an arrest, the investigation remains at an early stage and we are continuing to appeal to anyone who has even the slightest bit of information, or even CCTV or dash-cam footage, to please come forward.”
Inspector Ben Lawrence, who has led reassurance patrols in the local community following the fire, added: “These are clearly very sad circumstances and our thoughts continue to be with the family of those involved.
“This has also been an extremely traumatic event for the local community, especially for neighbours who have been left shocked and deeply saddened by the deaths of two very young children.
“We’ve increased reassurance patrols in the area and if anyone has any concerns we’d encourage them to speak to one of our officers.”
Nottinghamshire Fire and Rescue Service’s Group Manager Chris Clark said: “All of our thoughts are with the family of those involved and we send our deepest condolences.