Pettersen, who will be replaced in the side by assistant captain Catriona Matthew, had been receiving treatment since arriving in Des Moines, Iowa, for the biennial contest against the United States, who are 2/5 to win the trophy with Sky Bet, while Europe are 5/2 with the tie (14-14) 12/1.
However, the 36-year-old was still suffering persistent pain from a slipped disc on Wednesday and had little option but to pull out of Annika Sorenstam's side.
"I have made this extremely difficult decision to help the European team and give my team-mates the best possible chance of success," Pettersen said.
"There was no guarantee that I would be fit to compete on Friday morning and I did not want to play unless I was able to give 100 per cent.
"I truly love the Solheim Cup and I will stay and support my team this week in whatever way I can."
Sorenstam nominated Matthew - a 16/1 chance to be Europe's top scorer - as her alternate when she selected her four wild cards after the Ricoh Women's British Open earlier this month.
She said: "It's unfortunate that Suzann has to withdraw due to her back injury. The Solheim Cup has been such an important part of her career. It was a very tough decision, but I am proud of her and she will still be a leader this week.
"Catriona is a proven Solheim Cup performer who will be able to step right in and play with anybody. She's ready to go."
Pettersen was at the centre of a controversial incident in the 2015 Solheim Cup in Germany, which the United States used to fuel a brilliant fightback from 10-6 down to avoid an unprecedented third straight defeat.
In a fourball match carried over into the final day, Pettersen and Charley Hull were all square with two to play against Brittany Lincicome and Alison Lee.
Lee missed a birdie putt to win the 17th and, after the ball finished two feet behind the hole, scooped it up with her putter thinking it either had been, or was certain to be, conceded.
Hull gave that impression as she was already walking across the front of the green towards the 18th tee, but Pettersen said they had not conceded the putt and therefore won the hole.
European captain Carin Koch approached the match referee on the 18th to ask if there was anything she could do and was told they could concede the hole, but opted not to after Pettersen insisted she was not going to concede Lee's putt.
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