More than 20 firefighters battled to control the blaze at Belhaven Bay in the early hours of Saturday morning.
Contractor Maxi Construction had almost completed a £250,000 contract for the new visitor facilities.
A Lothian and Borders Police spokesman said: “This was a wanton act of vandalism that has destroyed a facility that was being built for use by the general public, and we are keen for any information that can help us trace whoever is responsible.
“We are appealing to anyone who noticed any suspicious activity in the area in the early hours of Saturday morning to contact police. Anyone else who has any other information that can assist our enquiries should also get in touch.”
A spokesperson for East Lothian Council said: “It’s a real shame that this has happened.
“This was not just a toilet block but had outdoor showers for swimmers and surfers plus storage facilities for local sports groups – so would have been a real asset to the local community and visitors to the area.
“It was very near completion but has been totally destroyed. We hope that anyone with information on who is responsible for this contacts the police.”