Michaela Haining, who was three weeks old, was taken to Raigmore Hospital but died on Thursday afternoon.
The death is currently being treated as unexplained and officers remain in the local area as the investigation continues.
Det Insp Brian Geddes said specialist officers, including experts in forensics, were assisting.
He said: "We have been conducting a number of inquiries in the local community as we try to establish the full circumstances surrounding Michaela's death.
"Specialist officers, including forensic officers have been involved in the investigation so far and will continue to be in the area over the next few days.
"I'd like to thank the community for their patience while these inquiries continue."
A baby whose death in Inverness is being investigated by police has been named.