Nystrom, who cleared re-entry waivers Wednesday afternoon, had four goals and eight assists for the Wild during the 2010-11 season. He played the previous four seasons with the Calgary Flames, and he has career totals of 23 goals and 28 assists.
The acquisition of Nystrom, who is in the second year of a three-year contract and has a cap hit of $1.4 million, will help keep the Stars above the salary cap floor when the team becomes healthy later this week.
Nystrom, 28, began this season with the Wild's AHL affiliate in Houston.
"We're going to evaluate," Stars coach Glen Gulutzan said. "Both guys felt pretty good today. We have to be real sure with what we're doing because you've got two guys that haven't played and have gone through only one practice. We've got to make sure they are completely healthy before we jam both of them in the lineup."
With Pardy about to come off injured reserve, the Stars were forced to sign a player to avoid dropping below the lower limit of the NHL's salary cap.
To make room for Nystrom, the Stars sent Tomas Vincour to the Texas Stars of the AHL.
Mark Stepneski covers the Dallas Stars for ESPNDallas.com.