Police have confirmed they received a report from North West Ambulance Service regarding an incident at 4.30am on Tuesday at a property at Backbarrow.
A four-month-old child was taken to Furness General Hospital, Barrow, but died.
Police said inquiries are continuing and residents may see an increased police presence in the area.
A 36-year-old woman and a 38-year-old man have been arrested on suspicion of causing or allowing the death of a child.
A police spokesman said: “Two people have been arrested as part of an ongoing investigation into the death of a four-month-old boy in Backbarrow.
“On 20 February at around 4.30am, police received a report from North West Ambulance Service regarding an incident at a property in Backbarrow.
“The child was taken to Furness General Hospital but sadly passed away.
“An investigation is underway by a dedicated team of detectives and other specialists in order to establish the full circumstances of the death in full consultation with the coroner.
“A 36-year-old woman and a 38-year-old man have been arrested on suspicion of causing or allowing the death of a child. They have been released on bail.
“Enquiries continue and residents may see an increased police presence in the area.”