The USA captain has broken down with a back injury and is now having surgery after participating in the Copa America.
“He finished the season with an injury in his back,” said Cherries boss Andoni Iraola.
“He wanted to play Copa America because it was very important for him, but he had restrictions and was still in pain, so two days after they were knocked out, he had surgery.
“He is out for some time. It is difficult to say how long but he won’t be fit for the start of the season. But September? October? I don’t know.”
Asked why Bournemouth did not stop Adams from joining up with the USA, Iraola said: “It was not our choice. It is a decision for the nations, who are allowed to select players, and he wanted to play thinking the injury would get better but he felt it was getting worse.”