A man is in police custody after a baby boy reported missing from his West Australian home died while being taken to hospital.

Police and ambulance were called to the Fortescue Roadhouse southwest of Karratha on Wednesday afternoon after the man arrived there with a 10-month-old boy who was not breathing.

The baby was being rushed to Nickol Bay Hospital when he died.

The 25-year-old man is in custody but police say no charges have been laid.

The child had earlier that day been reported missing from his Broome home after being collected by a man who his mother knew.