The Institute issued the most severe Class 3 warning on Saturday for areas around the Sangis River. They also issued a Class 2 warning around many other rivers in Norrbotten, the northernmost county in the country.
The Råne and Kalix rivers continued to rise on Saturday, while the waters receded in the Torne River near the city of Pajala.
"It's still an extreme situation," Kean Foster, at SMHI, told news agency TT.
SMHI expects the waters to continue to recede and stabilize during the next few days.