The Rangers, who entered Friday night's home game against Tampa Bay in 11th place in the East, are seven points out of a playoff spot. Dupuis, a left-winger, had 10 goals and three assists in 48 games this season.
"I think it'll be good for both teams," Minnesota coach Jacques Lemaire said after Friday's practice.
Dupuis has been with the Wild since being called up from the minors late in their inaugural 2000-01 season, but his production and playing time has dwindled since a career-best 20-goal, 28-assist output in the 2002-03 season.
On Monday, the Rangers traded Jason Ward to the Los Angeles Kings for rugged forward Sean Avery as part of a five-player deal. New York has been looking for a centre to play with second-line forward Brendan Shanahan.
The Rangers are expected to be busy leading up to the Feb. 27 trade deadline.
Dupuis, 27, already has matched his goal total of last season. He scored three goals in his final six games with Minnesota.
Hall, 26, never fit in with the Rangers, who acquired the left winger from Nashville in the off-season. He had four goals and eight assists in 49 games and was scratched from the lineup for Tuesday's loss at New Jersey. It was the fifth time in nine games that Hall was benched.
Hall will play for the Wild in Saturday's game against Carolina. Lemaire said he liked his size and aggressiveness after watching him play for the Predators in the 2005-06 season, when he had 14 goals and a career-high 15 assists in 75 games.