The draw, which was made in New York today, has resulted in the Scotsman facing Haase once again following their meeting at the Grand Slam in 2011.
Murray, who is seeded eighth for the competition, managed to beat the Dutchman in five after suffering a two-set deficit during their clash three years ago.
The former US Open champion was bumped up in the seedings following the withdrawal of Rafael Nadal to a wrist injury.
Haase, who is currently ranked 70th in the world, has never progressed past the second round at the tournament at Flushing Meadows.
Murray could potentially face world number one Novak Djokovic at the quarter-final stage, while Roger Federer could go up against Girgor Dimitrov, David Ferrer may have to play Tomas Berdych and Stanislas Wawrinka could possibly be drawn against Milos Raonic in the final eight.
The tournament will get underway on Monday.