Fritsche had a goal and four points in 16 games with the Rangers this season.
Over five seasons in the NHL, the 23-year-old has 30 goals and 67 points in 222 games with the Columbus Blue Jackets and the Rangers.
"Dan is a versatile player who can play center or wing, a determined player who makes the game harder on the opposition, and a winning player," said Minnesota general manager Doug Risebrough.
Reitz, 26, had a goal and an assist in 31 games for Minnesota this season, his third in the NHL.
The Wild also assigned center Krys Kolanos to Houston of the American Hockey League.