Irving initially suffered the injury during a pickup game in the offseason, McMenamin notes.
The 27-year-old was guarding the Los Angeles Lakers' Rajon Rondo closely along the sidelines and was caught by the arm of the ball-handler. He immediately removed his protective mask in discomfort, requested to be subbed off, and appeared to be in pain while on the bench.
Irving was making his first appearance for the Nets since signing with the team as a free agent this summer.
The Nets and Lakers are playing in Shanghai in their first of two scheduled preseason matchups in China; the second is penciled for Saturday in Shenzhen.
Thursday's game was allowed to go ahead despite the ongoing tensions between the NBA and China, though the Chinese government has reportedly barred media availability for players and commissioner Adam Silver.