The lovers, who played a married couple in season 2 of FX's anthology series "Fargo", got engaged over the Golden Globe weekend, reported New York Post.
Other details are still not available as their representatives have not responded to request for comment.
Dunst and Plemons first sparked dating rumours when they were spotted kissing in May, a few months after she split from her boyfriend of four years, Garrett Hedlund.
The two were later seen kissing at an Emmys after-party for their FX show "Fargo" in September.