The bodies were discovered in the Peristeria area in the south of the island, where one of the fires broke out. Authorities believe the victims were a couple.
A second fire was reported in Selinia, with the two blazes breaking out almost simultaneously and threatening homes and other buildings.
Four evacuation orders were issued as firefighters battled to prevent the flames from spreading further through the island. Residents and visitors in affected areas were urged to leave, while police were deployed to help people reach safety.
“There are hundreds of bathers and permanent residents, an evacuation order has been issued,” Fire Department deputy spokesman Yiannis Artopios told Greek broadcaster ERT.
Mr Artopios described the situation as a difficult fire burning within an inhabited area.
Strong winds have made the operation particularly challenging, with firefighters working to prevent the two fire fronts from spreading towards mountainous areas and potentially joining together.
Homes have been damaged by the flames, while several people have required medical treatment. Local reports said people were taken to a health centre after suffering burns.
A large emergency response has been launched, with hundreds of firefighters supported by fire engines, aircraft, helicopters, volunteers and water tankers. Coastguard vessels and other boats have also been deployed as authorities prepare for the possibility of evacuating people from threatened coastal areas by sea.
Salamina, located just west of Athens, is particularly busy at this time of year as people travel to the island during Greece's August 15 Assumption holiday.
The island had been placed under a high wildfire risk warning before the fires broke out.
The cause of the fires has not yet been established.
The latest deaths come during a difficult wildfire season for Greece, where strong winds and dry conditions have contributed to a series of major fires in recent weeks.
Authorities said dozens of fires had been reported across the country over the previous 24 hours, placing further pressure on emergency services.
The situation on Salamina remains ongoing, with firefighters continuing to battle the flames and authorities monitoring the risk to populated areas.
