The rain will mostly hit the Uppland coast and the southern side of the Norrland coast, Swedish weather agency SMHI said on Monday.
The agency issued a class one warning, the least severe of its three-stage warning system.
"The rain will continue northwards throughout the night and will hit northern Norrland by the start of Tuesday," Lovisa Andersson, meteorologist at SMHI, told the TT news agency.
She told the Aftonbladet newspaper that the rest of the country can expect similar conditions.
The good weather, however, is not far away. The agency has predicted temperatures as high as 20C in Stockholm through to Friday, the early 20s for Malmö, and up to 25C in Gothenburg.