"I exercised poor judgment," Griffin told reporters. "It's something I feel awful about."
Griffin broke the fourth metacarpal bone in his right shooting hand striking Testi, a close friend, during a night out while the Clippers were on the road in Toronto.
"It's something I think about every day and wish I could take it back," Griffin said. "I've told Matias that."
Griffin's expected to be out until at least the end of February. Clippers coach and general manager Doc Rivers said Tuesday the power forward won't miss the rest of the season, but added there's no timetable yet for his return.
Since the incident, trade rumors have swirled around Griffin, which Rivers shot down again Tuesday.
Griffin was out for 13 games prior to the punching incident with a quad injury. The Clippers have performed better than anyone expected in his absence, going 18-5.