Johnson, the U.S. Open champion, is favourite to win the Masters title after victories in his last three tournaments.
"At roughly 3:00 pm today, Dustin took a serious fall on a staircase in his Augusta rental home," Winkle said in a statement.
"He landed very hard on his lower back and is now resting, although quite uncomfortably. He has been advised to remain immobile and begin a regimen of anti-inflammatory medication and icing, with the hope of being able to play tomorrow. I will refrain from commenting further until I know more about Dustin's condition."
The Masters starts in Augusta on Thursday with Johnson scheduled to play alongside fellow Americans Bubba Watson and Jimmy Walker in the last group out.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
No world number one has captured the Masters Green Jacket since Tiger Woods in 2002.
"It's a funny game. It doesn't matter how good you're playing, you can still not win," Johnson, who became world number one in February, said on Tuesday.
"I've got a lot of confidence in my game right now, especially with the way I've been playing the last few tournaments. But, you know, anything can happen."
Apart from top-10 finishes the last two years, Johnson has a modest record at the Masters.
His dreams of winning last year were ruined by two double-bogeys in the final round. He tied for fourth, four shots behind winner Danny Willett.
It is not the first time Johnson's bid for a Green Jacket has been hit by injury.
The big-hitting American was forced out of the 2012 Master after injuring his back while lifting a jet ski.
(Editing by Steve Keating)
