Six fire engines were called to the burning building in the grounds of the park off Shady Lane at around 3.20am.
Crews from Bamber Bridge, Penwortham, Chorley, Preston and Fulwood tackled the fire and no injuries have been reported.
Firefighters used two hose reels and four breathing apparatus to extinguish the fire, which reportedly started underneath the building.
The fire service said the cause is believed to be suspicious and it is being investigated alongside police.
"It has been reported to us and the cause of the fire is under investigation alongside the fire service," confirmed a Lancashire Police spokesman.
It is not clear how much damage has been caused, but the park management say both the cafe and visitor centre will stay closed "until further notice."
"Due to unforeseen circumstances the visitor centre and Cuerden View Cafe are closed until further notice," it was confirmed on Facebook this morning.
A fire service spokesman added: "Six fire engines from Bamber Bridge, Penwortham, Chorley, Preston and Fulwood were called to a commercial fire on Berkeley Drive, Cuerden.
"Firefighters used two hose reels and four breathing apparatus to extinguish the fire. The cause of the fire is under investigation and no injuries have been reported."
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