The Italian was due to begin his campaign against Britain's Arthur Fery at the ATP 500 tournament, which got underway in Tokyo on September 30.
Musetti confirmed the setback in a social media statement, saying the injury occurred during a training session and expressing his disappointment at missing the tournament.
The 24-year-old said he had been looking forward to returning to Tokyo and playing in front of his Japanese fans.
He also indicated that his immediate target is to recover in time for the Shanghai Masters, adding that he would do everything possible over the coming days to be ready for the ATP Masters 1000 event.
The withdrawal represents another interruption to Musetti's 2026 season, which has already been affected by several physical setbacks.
The Tokyo tournament runs from September 30 to October 6, with the ATP Tour listing it as a 500-level event.