But fearing disruption of bread supplies, the government will allow his businesses to open new bank accounts under supervision, government spokesman Jolino Makelele told a press briefing.
The US sanctions target Saleh Assi, who is based in the Democratic Republic of Congo, and a compatriot, Nazem Said Ahmad, a Lebanon-based diamond dealer and art collector.
In a statement last Friday, the US Treasury Department accused the pair of being "money launderers" who had generated "tens of millions of dollars for Hezbollah, its financiers, and their malign activities."
Assi's assets and those of "all of his businesses" will be frozen, along with "all transactions from these accounts", Makelele said after a special cabinet meeting.
The businesses will be placed under "an independent administrator until a lasting solution is reached, in line with the requirements of the US Treasury Department's decision," he added.
The companies will have a special dispensation to open new bank accounts, but under government supervision.
This is to "avoid damaging effects... on the economy and public," Makelele said, referring to the supply of bread by Assi's mega-bakery to the 10 million residents of the capital Kinshasa.
The United States considers Hezbollah a "terrorist" organisation. The group is also a key political player in Lebanon.
Washington has targeted the Shiite party with tough sanctions, ramped up under the administration of President Donald Trump.
A sworn enemy of neighbouring Israel, Hezbollah is the only faction not to have disarmed after Lebanon's 1975-90 civil war.
Early last year authorities in the DRC forced Assi to abandon a plan to hike prices, which they said would destabilise the country.