Between 5 to 10 centimeters of snow has fallen in the capital, and more is on the way.
“There are reports of a large number of accidents, thankfully without any serious injuries so far,” says Traffic Administration spokesperson Denny Josefsson to Swedish Radio.
The motorway north of Stockholm, the E18, is blocked by a stuck tanker. The same highway is affected by a lorry accident outside Örebro, west of Stockholm.
Emergency services are expected to clear the road by the afternoon.
Another lorry has caused traffic problems on the E4 between Norrköping and Nyköping, northbound.
In Stockholm the snow is causing trouble for bus services, with several lines cancelled or hit by delays. Only lines 1-4 are running in central Stockholm.
In the south of Sweden police are dealing with around 20 accidents, says spokesperson Fredrik Bratt to news agency TT.
Airport operator Swedavia says "disruptions may occur" in flights to and from their arirports, which include Stockholm's Arlanda and Gothenburg's Landvetter.
Snow is expected to keep falling, especially along the east coast, says the meteorological agency SMHI.