The 25-year-old last played during Wimbledon in July, where he won his sixth Grand Slam, and has been missing from the tour ever since.
In a statement posted to his social media, the Italian said: "Even though I have been working hard with my team and my medical staff, we have now had to make the difficult decision that I will not be able to compete at the US Open this year.
"We have been back on court in Monte Carlo over the last couple of days and have realised that I still need more time to recover from my right knee issue. I’m obviously very sad and disappointed, as New York has a special place in my heart.
"I was very much looking forward to coming back and playing in the electric atmosphere in front of the great fans there."
The news comes just days after Carlos Alcaraz confirmed his participation at Flushing Meadows, with his fitness also in question over the last few weeks.
The US Open gets underway on Sunday, with the final on September 13th.