The same parking regulations apply for motorcycles, mopeds class I, and cars. 

Swedish parking legislation is stated in the Road Traffic Regulation Act (Trafikförordningen) and applies to the whole country. Separate motorcycle parking areas are often marked with signs. When there is a motorcycle symbol below the parking sign, only mopeds class I and two-wheeled motorcycles without sidecar are allowed to use the parking space. In parking areas with a time limit, the same limit applies to motorcycles as to cars. More than one motorcycle can be parked in the same parking spot, but the parking fee must be paid for each vehicle. You’ll pay the parking fee that applies to the particular parking space and if you have a paper ticket, it must be clearly visible on the motorcycle. You can place the ticket in a plastic pocket on the gas tank, or in a special ticket holder that is fastened on the shackle lock. 

If there is no designated motorcycle parking in the car park, you should follow the parking rules that apply to cars.