"Adjust your speed and make sure to keep a safe distance from the vehicles in front of you," Swedish Transport Agency (Trafikverket) spokesman Denny Josefsson told the TT news agency.
"Road conditions may be difficult in certain areas."
The E4 motorway outside of Helsingborg remains closed in both directions following Tuesday's devastating 100-car wreck which killed one person and sent more than 40 to hospital.
It remains unclear how much more time will be needed to remove all of the vehicles, many of which were trucks, from the roadway in order to reopen the E4.
In addition, the wreck damaged guardrails and beams on the Tranarpsbron bridge, further complicating projections on when the road will reopen.
"The initial projection is that the western section of the brigde will be opened for traffic sometime on Wednesday. And when the road is opened, there will likely be a reduced speed limit," Josefsson told TT.
However, he added that it will likely take "one to two days" before the eastern section of the bridge will reopen an account of the damage it sustained during Tuesday's wreck.
Meanwhile in central Sweden, the E18 motorway was closed down overnight between Västerås and Köping while crews continued to clear the stretch following a series of accidents involving trucks.
The Transit Administration warns of slick road conditions in many parts of central and northern Sweden.
In particular, the authorities have warned drivers to beware of black ice.
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"Many people don't see it and think that if it looks like normal asphalt, it is asphalt and don't see the layer of ice. But it's hard to predict where it will crop up," Joseffson told the Aftonbladet newspaper.
While snow has tapered off in most of the country, isolated snow showers are forecast for Sweden's east coast on Wednesday, with temperatures expected to remain below freezing across the country.