Allen underwent successful arthroscopic surgery on his right ankle Wednesday, the team announced, just five days after the Celtics' season ended with a Game 7 loss to the Miami Heat in the Eastern Conference Finals.
Mickael Pietrus, who had right knee surgery last July, had arthroscopic surgery on the same knee Wednesday.
"That's my first priority, just going into surgery sometime," Allen said Saturday after the Celtics' 101-88 loss. "If I could do it tomorrow, I would do it tomorrow. That's probably my main concern right now, is taking care of that. My body feels good. That's been my only issue. After that, it's hard to say."
Both surgeries Wednesday took place at New England Baptist Hospital and were completed by Celtics team physician Brian McKeon and assisted by Mark Slovenkai.
Allen missed 17 games from March 22 and May 4, with a brief five-game return in between, due to pain from bone spurs in his right ankle. Pietrus battled knee soreness almost continually after returning from a two-week absence due to a concussion and immediately playing three games in four days, which caused his knee to flare up.
There have been murmurs about Allen's possible retirement this offseason, but the promptness of this procedure could indicate that the 16th-year veteran is serious about getting back on the court. The time of Pietrus' procedure is also key to him making it back for training camp this fall. Pietrus' recovery from surgery to remove loose bodies from his right knee last summer took longer than expected, and the Toronto Raptors nixed a trade with the Phoenix Suns in December over concern that Pietrus had not fully recovered. The Suns subsequently placed Pietrus on waivers, where the Celtics picked him up Dec. 24.
Both Allen and Pietrus are due to become free agents. Teams can begin signing free agents July 11.