Analysts fear the arrest could create a leadership vacuum at the group.
But the Czech Industry and Trade Ministry said it had received a confirmation from Hyundai that the plan to build the €800m to €1bn factory in Nosovice would go ahead.
"After several phone calls and letters to the Korean government, we received a written document in which Hyundai confirms its investment in the Czech Republic and that they accept our proposal to sign the contract in Korea," CTK quoted Industry Minister Milan Urban as saying.
"The agreement will be signed in mid May," he added.
An Industry Ministry spokesman was not immediately available for comment.
Urban said Hyundai had said the investigation in Korea would have no impact on the company's Czech plans.
The Hyundai factory should come on line in 2008 and employ about 3 000 people directly and create around 12 000 further jobs at suppliers' plants and in services.