Johnson, a five-time PGA Tour winner who is No. 12 in the world, described the injury as a "tweaked back" on Twitter.
"You have no idea how much I wanted to walk the fairways at Augusta and fulfill what I've been practicing for!! I'll have to root my buddies!" he tweeted.
His agent, David Winkle at Hambric Sports Management, said Johnson first had back pain in January when he withdrew from the Humana Challenge, and played through minor pain the next six weeks.
"His back bothered him from time to time. He kind of played through the pain, but it was never crippling," Winkle said in a voicemail. "He rested it at Bay Hill, got back to working some last week, and tweaked it last week lifting a jet ski."
Johnson, who was born in Columbia, S.C., and lives in south Florida, had been going through therapy and taking anti-inflammatory medicine. Winkle said he will be seeking opinions from other doctors and "hopefully, it's nothing serious."
"At the same time, it did knock him out this week," Winkle said. "Needless to say, he's pretty bummed out at this point."
Johnson has come close to winning every major except the Masters.
He had the 54-hole lead in the 2010 U.S. Open at Pebble Beach until an 82 in the final round. He had a one-shot lead playing the final hole at Whistling Straits in the 2010 PGA Championship until it was discovered he grounded his club in a bunker and was given a two-shot penalty. A year ago at the British Open, he was closing in on Darren Clarke until hitting his second shot out-of-bounds on the 14th hole. He tied for second.
Johnson has never finished higher than a tie for 30th at the Masters.