Isner was battling what he called "a bit of tendonitis" all week and his withdrawal ahead of the singles match against Spain's Fernando Verdasco also ended team mate Venus Williams's hopes of emulating sister Serena's 2008 Hopman Cup victory.
"I'm very, very sorry to all the fans here, I really wanted to play here against Fernando, so I apologise for that and I hope you guys understand," said Isner, who became the second player to quit the tournament.
Germany's Andrea Petkovic pulled out on Sunday with a knee injury.
"I absolutely love this event, it's my third time here and it's very disappointing for me and it's a tough one to swallow but for me, first and foremost I've got to try and get 100 per cent healthy," Isner said.
Following his withdrawal, Spain were awarded the tie and go through to Saturday's final as the top-placed team from Group B.
Isner was optimistic of playing the Australian Open later this month.
"My plan now is just to treat it as best I can and see how it reacts," he said.
"I do know I've always been a fast healer when I've had little injuries pop up here and there, so I'm confident I'm going to be fine for the Australian Open.
"It's not a great way to start the year but I'd rather it happen this week than in two weeks (at the Australian Open)."
Australian junior Thanasi Kokkinakis was named Isner's replacement in the American team.
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- Fernando Verdasco