Police and St John Ambulance paramedics attended the scene and found a boy and a man had died.
Paramedics found the woman nearby, "in need of urgent medical assistance", police said.
ABC is reporting a gas fridge is believed to have caused the tragedy, with the appliance also killing the family dog.
In a statement, police said they were not treating the deaths as suspicious and initial investigations suggested there had been a fault with camping equipment, inside the family's tent.
WA's Department of Fire and Emergency Services also attended the scene to safely remove the faulty camping equipment.
The family had been sleeping in the tent yesterday morning when tragedy struck.
Police would like to speak to anyone who was camping in the area.
The investigation is ongoing, and a report will be prepared for the Coroner.
Wedge Island, located 160km north of Perth, is popular with campers and 4WD enthusiasts.
The remote, white sand island is now home to more than 350 beach shacks, with holiday-makers visiting for the past 70 years to fish, snorkel and kitesurf.
"The community has autonomously and democratically addressed the many issues a community has to face to survive in such a remote location. Issues such as harvesting water and power, protection from the elements, first aid and firefighting to name a few," the island's website reads.