"Patrick is still in hospital but feeling much better.
It has been very scary the last few days, and at the moment we do not have a timeline for his recovery, "said Ms Justine Reed in a statement.
Patrick Reed, 31 years old, is ranked 17th in the world.
As he misses the competition, which is the last chance for the players to take a place in the Fedex Cup play-offs, he cannot automatically qualify for the American team in the Ryder Cup.
There is still a chance to participate, if team captain Steve Stricker gives him a free ticket.