The 38-year-old Hafeez has been told to rest for two weeks before he can resume training of any sort.
The problem facing the senior player is that the national team head coach Mickey Arthur has set April 14 as the deadline for the players to undergo their final fitness tests before considering for World Cup selection.
The Pakistan squad is also due to leave early for England -- around April 24 -- to play practice games, a five-match ODI series against England and two warm-up matches against Bangladesh and Afghanistan before the World Cup kicks off on May 30.
"Hafeez had to go for the second surgery as the fracture in his left thumb had not healed properly and the surgeon Mike Hayton had advised him for a follow-up procedure," one source close to the former skipper said.
An official in the Pakistan Cricket Board said if the head coach and chief selector Inzamam-ul-Haq wanted, they could allow Hafeez to recover completely and take his fitness test later on after the deadline for all the players.
"There is still plenty of time before the World Cup begins, so it all depends on how Arthur and Inzi handle the issue. If they feel Hafeez's selection is important for the team's chances in the World Cup, then most probably they will give him ample time to recover from his injury," he said.
The official said it would be difficult for Hafeez to be 100 percent fit when the fitness tests are conducted on April 14 in Lahore.
Inzamam has said that Hafeez would be a key player for Pakistan in the World Cup.
Hafeez fractured his right thumb while attempting a catch of his own bowling in his second match of the Pakistan Super League in which he was captaining the Lahore franchise. Scans later revealed a fracture and the need for surgery.
Hafeez, who has retired from Test cricket after 55 matches, has already appeared in 208 ODIs and 89 T20 Internationals.
First Published: March 28, 2019, 10:27 PM IST