Police were informed of a fire at the historic attraction, which is thought to be the world's oldest theme park, at 8:34pm on Wednesday.
A small area around the scene of the fire remains sealed off on Thursday.
Bakken director Nils-Erik Winther said the amusement park would open as normal at 11am Thursday.
“There will be a small area around where the fire was that will be closed off, but everything else was fortunately unharmed,” Winther said.
Both police and fire services were dispatched to the scene Wednesday after the fire broke out, with up to 45 firefighters and 15 fire engines attending the blaze, fire service Beredskab Øst confirmed.
All guests were evacuated during the fire.
“It's sad when something burns down but on the other hand, I'm pleased there was only material damage,” Winther said.
The park CEO praised staff and guests for their response during the incident.
“Staff guided guests out of the restaurant and Bakken was evacuated. It was very impressive to see that people were so calm and everyone respected the cordons,” he said.
The fire was “completely under control” by 9am on Thursday, fire services said. The cause of the fire will be investigated.
The park is open every day until 9pm this week, breaking with its regular seasonal opening during the school autumn holiday.
Bakken is the second-most visited tourist attraction on Zealand after the Tivoli amusement park in central Copenhagen. Its history dates back to 1583, when a natural water source was discovered in the area and it became a desired destination for local residents and Danish nobility.
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