The 2.5MW to 3MW vessels will cost RUB 7.9bn ($195m), Russian media said.
Delivery will be completed by the end of 2018.
The port of Astrakhan will take the first, followed by Arkhangelsk, Novorossiysk and Petropavlovsk-Kamchatsky.
Yards groups that failed to win the business included Vympel and United Shipbuilding Corporation.
Nevksy, based in St Petersburg, is part of North-Western Shipping, owned by tycoon Vladmir Nisin's UCL Holding.
