Officers were called to Skien Leisure Park, in Norway’s southern Telemark region, at about 9.20am BST (10.20am local time).
Images posted online show armed officers guarding the park’s entrances, with a police helicopter also at the scene.
Hjalmar Johansen High School, which is located near the park, has been placed on lockdown while police hunt for the man.
The suspected gunman is said to be wearing camouflage clothing, according to local media.
In a statement posted on Twitter, south-east Norway’s police force said: “An armed man has been spotted in Skien Leisure Park.
“People have been requested to leave the area. The police are at the scene. There have been no threats or shots fired.
“There is a large police presence in place and all emergency services have been notified.
“Children at schools and kindergartens in the vicinity around the leisure park are kept in safety indoors until further notice.”
Police station manager Dag Storksen said: “I can confirm we are investigating reports of an armed man in uniform-like clothing.
“There are several things we don’t know about the man, so we need clarification. We’re receiving resources from all over the country.”
Hjalmar Johansen High School tweeted: “An armed man has observed out in the woods in Skien Leisure Park today.
“All the students at the school are safe inside and the doors are locked. The police are on the site and are keeping the school informed.”
Parents of pupils are being updated with the latest information via text.