Ally McDonald, who was named as the first alternate when the team was finalised last month, will replace her for the three-day event, starting on Friday at Gleneagles in Scotland.
Lewis, a former world number one and four-time Solheim Cup veteran, was named to Team USA as one of Inkster’s two captain's picks.
Inkster told lpga.com: "Stacy is one of the fiercest competitors I have ever met. I know this was an incredibly tough decision for her, but she also has the team's best interests at heart.
"Stacy will stay with Team USA over the next week and will still be an incredible asset to our crew. But when I had to choose an alternate, I knew Ally would be able to step up for the challenge. She's got a cool head but a fiery spirit. I know she'll bring her best to Team USA."
"I’m extremely disappointed not to be able to play," said 34-year-old Lewis, currently ranked 81 in the world. "I’m a competitor and I want to play, but I had a back injury flare up last week."
"I've done everything I could possibly do over the last week to be ready to play. For my health and what I feel is in the best interest of the team, I decided to take myself out."
The Solheim Cup pits the best women players from Europe and the United States against each other in matchplay format.