As well as Stockholm, a class one warning has been issued in Östergötland, Södermanland, Västmanland, and Örebro. The highest possible warning is a three.
While snow is common in Sweden in winter, national weather agency SMHI only issues warnings when there is a chance that it could cause dangerous conditions.
“It will snow for a long time and it will be a continuous snowfall. Most snow will fall on the day [Wednesday] and slow down tomorrow,” Sandra Andersson, a meteorologist at SMHI told the TT news agency.
The snow is expected to be wet and heavy, rather than the pretty, white and fluffy kind.
SMHI said that due to low temperatures, it was likely to linger on the ground for several days.
“It's always hard to say, but the temperature is around zero, so it'll probably be a while,” said Andersson.
In Östergötland – about two hours south of Stockholm – police have issued a separate warning asking drivers to be careful in snowy weather.
Temperatures have dropped below -5C most nights in southern Sweden over the past fortnight, with snow that fell over last week forming dangerously icy transparent patches on roads and pavements in some parts of the city.
There were several road accidents on Friday morning, including one involving a bus carrying school children, which flipped over to the west of the capital.
Last week, Stockholm Cty Council announced plans to introduce 'gender equal' snowploughs, designed to make pavements and other pedestrian areas (which are frequented by more women and children than men), just as safe as the city's roads.