A baby rushed to hospital on Saturday with critical injuries has died in Starship Hospital. 

The four-month-old baby was taken to Invercargill Hospital on Saturday morning and later transferred to Starship Hospital in Auckland. 

Police said in a statement this morning that the baby passed away at Starship yesterday. 

"A homicide investigation is now under way in relation to how the baby received the injuries," police say. 

Officers are still speaking with residents of an Elizabeth St, Invercargill property and "no one else is currently being sought". 

Scene examinations were carried out earlier this week. 

"Police's thoughts are with the baby's whānau," the statement said. 

"The family have requested privacy at this difficult time."