The worst of the rain was centred on the Småland region. Large areas around Jönköping are flooded:
"A dam has just burst in Aneby and several are threatening to do so in Jönköping County," said Fredric Jonsson of Jönköping's emergency services.
A further dam in Aneby, northern Småland, and another in nearby Nässjö are said by emergency services to be at risk of breaking.
"There is a significant risk and we are working to strengthen them, and have evacuated a number of homes near Flisby, to the south of Aneby," said Fredric Jonsson.
Another dam has broken in Habo, north of Jönköping, and a small industrial area has been flooded. Jonsson said that up to 20 millimetres of rain is forecast to fall over the next 24 hours.
"It's just drizzling now, and the flow of water has already eased off a bit," Jonsson said.
A number of minor roads and cellars have flooded in Småland since Tuesday night. Officials were for a time concerned that a dam in Bruzaholm, near Eksjö, would burst, flooding a village. The danger is now judged to have receded.
Swedish weather service SMHI has not currently issued any warnings of rivers bursting their banks.
"Before this rain arrived the ground was very dry and the water table is low. There is a risk that surface gulleys overflow," said meteorologist Kjell Lund.
The heavy rain eased somewhat overnight, but more rain is expected. A large low pressure area over Denmark at lunchtime on Wednesday was expected to move eastwards, but it was not immediately clear whether it would hit Sweden.
"It seems as though the heaviest part of it has passed to the south of us, but things are quite changeable at the moment," said Lund.
Rail operator SJ cancelled a number of trains during the morning and said forcing thousands of passengers on the Stockholm Malmö line and the regional Nässjö-Falköping line were forced onto buses for parts of their journeys.
"Around 7,000 passangers and 40 trains are hit by delays. This is affecting the southern part of the mainline between Stockholm and Malmö," said DJ's Edvard Lind.
Replacement buses are operating between Nässjö and Mjölby, leading to delays of one and a half to two hours.
"The Nässjö-Falköping line is affected because (track operator) Banverket has decided to prioritize freight traffic, meaning we have to thin out passenger traffic significantly," Lind said.