Under the €19m contract, Lemminkäinen will also be responsible for intakes, shafts and tunnels of the plants.
Work on the project is scheduled to commence this month with plans to complete in December 2016.
The contract is part of Småkraft’s Fjærland project, which involves development of six small-scale power plants along rivers flowing into the Fjærland fjord.
As part of the deal, Lemminkäinen will also construct intakes for two other plants, including approximately 2.5km of tunnel. The company will also build the power plants Lidal and Romøyri.
Lemminkäinen executive vice-president Harri Kailasalo said: "This contract is a good example of projects we want to be a part of and it supports well our strategic target to grow our infrastructure project construction business."
Smakraft is majority-owned by Norwegian state owned electricity company Statkraft.