The 31-year-old Carlisle spent Thursday night in hospital after suffering the fracture fielding against Somerset on Tuesday.
He will be sidelined for between three to six weeks. Carlisle, who had made three centuries on tour, played in the just-concluded Test series against England, won 2-0 by the home team.
"Stuart has been our most prolific batsman and is probably playing as well as at any time in his career," said Zimbabwe captain Heath Streak.
Steak said Stuart Matsikenyeri was in line to replace Carlise in the side. The 10-match triangular series begins on Thursday, June 26, with Zimbabwe meeting England at Trent Bridge.
