Squads of hunters will pursue the wolves in a three-month "battle" from 15 January, officials say.
The most successful hunters will get bonuses. The vast, sparsely populated region is also known as Yakutia.
Experts quoted by Russian media believe a shortage of mountain hares has caused the migration of hungry wolves.
Wolf packs have moved into Sakha's central reindeer pastures, from their normal hunting grounds in the mountains and dense forests. Reports speak of increased attacks on livestock, but not on humans.
The wolf-hunting season has been extended to the whole year, as the target is to get the wolf population in the region down to 500 - reckoned to be the optimal number. Currently there are estimated to be more than 3,500.
There will be a "six-figure sum" for hunters who bring in the most wolf pelts - a big incentive, as 100,000 roubles (£2,043; $3,280) goes a long way in a region that is famously cold, remote and under-developed. [more]