Sarfaraz Ahmed has been called into the tour squad as his replacement.
"Sarfaraz has been included in place of Umar who has been called back from the West Indies for medical checks," said a Pakistan Cricket Board official.
The official did not elaborate on Umar's medical problem but a family member who declined to be identified told Reuters that the player was on a flight to Jamaica when he had his epileptic fit.
Umar, 23, has played in 16 tests for Pakistan, scoring 1,003 runs at an average of 35.82. He has also featured in 76 one-dayers and 45 Twenty20s.
Pakistan will play two tests, three one-dayers and two Twenty20s in Zimbabwe. The opening game is a T20 international in Harare on Friday.
Test opener Imran Farhat has also withdrawn from the squad, citing domestic problems. He will be replaced by the uncapped Shan Masood.