Croatian Jelavic, Hull's top scorer in the league this season with six goals, sustained a knee injury during Saturday's defeat by West Bromwich Albion that left the club in the relegation zone.
"Scans have shown that (he) sustained no serious damage to his knee at West Brom on Saturday although he is expected to be sidelined for between three and six weeks," the club said on its website (www.hullcitytigers.com).
Uruguayan Hernandez was also a casualty of the defeat to West Brom, suffering a tear of his adductor muscle.
Jelavic and Hernandez have scored almost half of Hull's 20 league goals this season and manager Steve Bruce will probably look for back-up in the transfer window.
"Our injury list seems endless and we're finding it a struggle," he said at the weekend.
"We're always trying to improve and we will try to get a couple in - it's essential that we do that."
(Reporting by Martyn Herman, editing by Alan Baldwin)
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