The 32-year-old American star landed "very hard" after a fall down the stairs at his rented house in Augusta yesterday, his agent said, but still hopes to be fit enough to tee off in the first round.
Johnson is the oddsmakers favorite to collect the winner's green jacket at Augusta National after winning his past three starts.
"At roughly 3 pm today, Dustin took a serious fall on a staircase in his Augusta rental home," said his agent, David Winkle, in a statement. "He landed very hard on his lower back and is now resting, although quite uncomfortably.
Johnson is scheduled to tee off in Thursday's final first-round group at 2:03 pm alongside compatriots Jimmy Walker and Bubba Watson.
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Even if he is able to start, his trademark long driving skills could be compromised if the back trouble continues, a potentially serious handicap over the 7,435-yard Augusta National layout.
Johnson averaged a tournament-best 299.5 yards in driving distance last year, when he finished a career-best fourth, and averaged a Masters-low 26.50 putts per round in 2015, when he shared sixth.
"I don't know how many guys are in the field, but they are the best golfers in the world, so you've got to bring your best stuff if you want to win."
- Another setback -
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The injury marks another setback in the checkered career of Johnson, who won his first major title last year at Oakmont.
Johnson withdrew from the 2012 Masters after a back injury suffered, his agent said, when he lifted as jet-ski.
Even in his major victory last June, Johnson had to play the final holes knowing he would likely receive a penalty over an earlier infraction after a rules official had told him to play on.
Johnson became the world number one by winning at Riviera in February and followed with World Golf Championships Mexico and Match Play titles last month. He would be the first player since 1976 to enter the Masters on a three-event win streak.
The last time a world number one missed a major tournament was in 2015 when Rory McIlroy suffered an ankle injury a few weeks before he was to have defended his title at the British Open.
Johnson has not missed a major since the 2014 PGA Championship, which came just after he announced he was taking a six-month break from golf to seek professional help for "personal challenges."
Johnson hopes to make his seventh Masters start after unleashing a late charge on Sunday last year. He made birdies at the par-5 13th and 15th holes but a double bogey at 17 ended his chances to overtake eventual winner Danny Willett of England.