HIE along with other public bodies are to be run by a single board under Scottish government plans.
The government has said services already provided in the Highlands and Islands would be protected.
Scottish Lib Dem leader Willie Rennie unveiled the petition on a visit to Inverness.
He and his party argue that decisions on HIE should be taken by a board based in the Highlands and Islands.
In October, the Scottish government set out plans to reform Scotland's enterprise and skills agencies in a report on Phase 1 of its Enterprise and Skills Review.
It has proposed setting up a new single Scotland-wide statutory board to co-ordinate the activities of HIE, Scottish Enterprise and other public bodies.
HIE began as Highlands and Islands Development Board more than 50 years ago. It supports businesses and initiatives in the Highlands, Western Isles, Northern Isles, Moray and Argyll.
The Scottish Lib Dems have started a petition supporting calls for Highlands and Islands Enterprise (HIE) to keep its board.