The 22-year-old injured his foot during South Africa's three-day tour match on Friday. He stepped on a pebble and could only bowl five overs.
"X-rays have revealed that Morkel has suffered a fracture on his left foot and for further assessment he is due to return home as soon as possible," South African team spokesman Michael Owen-Smith told reporters
"Since this kind of injury takes six to eight weeks to heal, Morkel's tour is over."
Morkel was given fitness tests before the ongoing first Test against Pakistan, which started Monday. His place was taken by fellow paceman Andre Nel.
Smith said no replacement has yet been announced for Morkel.
"The selectors will decide whether to send a replacement," he added.
The second Test starts in Lahore from October 8.
South Africa also play five one-day internationals on the tour, for which a squad will be announced later.