Authorities are warning people to stay away from rivers and steep slopes as the downpour is set to continue for days.
Swedish and Norwegian meteorologists issued red alerts, the most severe warning level, covering several days this week.
They said the hardest-hit places could receive a month or more worth of normal rainfall in 24 hours – possibly triggering the worst floods in 25 years in Norway, and in 50 years in Sweden.
A train carrying more than 100 passengers derailed in eastern Sweden on Monday as the rain partly washed away the railway embankment, injuring three people who were taken to hospital, police said.
Gale force winds and thunderstorms knocked out local power lines and disrupted several Baltic and North Sea ferries as well as some air traffic, while Norway suspended certain train services and postponed a number of outdoor football matches.
Norway’s Prime Minister Jonas Gahr Stoere said he expected extreme weather events to become more frequent.
“This is an effect of climate change, with wilder and wetter weather in Norway,” Stoere told public broadcaster NRK.
Hitting Sweden on Sunday evening and reaching Norway on Monday, the low-pressure system was dubbed “Hans” by the Norwegian Meteorological Institute, which said naming the weather system makes it easier to get the public’s attention.
Authorities warned those most affected to stay away from rivers and steep slopes and only travel when strictly necessary.
They said there was a high risk of widespread property damage as the downpour was set to continue in the coming days.
Neighbouring Denmark also saw heavy rainfall and issued a yellow alert, a lower-level warning, while meteorologists in Finland said the country could see severe thunderstorms later this week.
Elsewhere in Europe, the death toll from days of heavy rains and flooding in Slovenia climbed to six on Monday.
Slovenia’s Prime Minister Robert Golob has described the torrential rains and severe flooding that hit the Alpine country of two million as its worst natural disaster since independence 30 years ago.
Flash floods and landslides that began on Thursday had submerged large swaths of central and northern Slovenia, cutting off access to villages and disrupting traffic.
On Sunday, emergency workers recovered the body of a 35-year-old man in a river near the village of Mirna Pec in the east.
Another man, who was taking part in the clean-up operations, was found dead after falling into a cesspit near the town of Kamnik close to Ljubljana, media reports said.
The bodies of two Slovenians and two Dutch citizens had been found earlier.