The 22-year-old suffered a fracture in his left index finger during a club match and doctors have advised him rest for the injury to heal completely, the Pakistan Cricket Board (PCB) said.
"It's a big blow for us as Jamshed was part of the T20 and one-day squad for the Sri Lanka tour," team manager, Naved Cheema said.
The PCB has not named a replacement for Jamshed yet.
Jamshed had made a comeback to the Pakistan team during the Asia Cup in March in Bangladesh after being sidelined for nearly three years. He had a successful tournament, scoring a hundred against arch-rivals India.
"It is hugely disappointing to miss out on such an important tour. But it is something beyond my control. I just need to be patient now," Jamshed said.
The Pakistan team began its formal training today at the Gaddafi stadium before the limited-over squad leaves on May 28 for Colombo.
Pakistan are to play two Twenty20s, five ODIs and three Tests on their tour of Sri Lanka starting early next month.