"I have to apologise to the fans and sponsors. With heartfelt regret, I won't be playing in the Masters due to a tweaked back," he said 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!”
Johnson will not be replaced in the field for the first major of the season.
His agent David Winkle added: "His back bothered him from time to time. He kind of played through the pain, but it was never crippling.
“He rested it at Bay Hill, got back to working some last week, and tweaked it last week lifting a jet ski.”
The big-hitting Johnson has had top-10 finishes in every major except the Masters. He lost the 2010 PGA Championship after receiving a two-shot penalty for grounding his club in a bunker on the final hole.