The Australian pulled out of his Wimbledon quarter-final against Novak Djokovic last month with a cartilage tear in his hip and subsequently missed the Paris Olympics.
He battled through his first round match at Flushing Meadows, beating home player Marcos Giron in four sets, but is no certainty to return to the court on Thursday, Australian media reported citing De Minaur's camp.
De Minaur had a light training hit on Wednesday but said he was struggling to change his game to protect the injury.
"It's super hard. I mean, for me, the actual concept of not trying to retrieve every single ball that's out there on the court, it is tough," he told the Australian media.
"I've been brought up with just going out there and trying to make every single ball back. So when you've got to play a certain type of way to look after yourself, it's also quite difficult.
"All of a sudden I'm having to think a lot more than I'm used to, and it makes it a lot tougher.
"So I'm learning to deal with it, play with it, have low expectations and just be mindful of it because it's still there."
De Minaur was mindful that his layoff after Wimbledon had cost him ranking points in the race to the ATP Finals in Turin in November where he is desperate to qualify for the first time.
"The goal, obviously, is Turin, and missing a lot of weeks on the tour, a lot of big tournaments, is very detrimental to your chances of making Turin," he said. "Because they're big points on offer and big events.
"So I wanted to make sure I was coming back as soon as possible but at the same time knowing that I'm not 100% it's not easy."
