Chilima, 51, was aboard a military aircraft with nine others that left Lilongwe, the capital, at 09:17 a.m. (0717 GMT), Malawi's Office of the President and Cabinet said in an earlier statement.
It said efforts by aviation authorities to make contact with the aircraft since it went off the radar had failed. The plane had been scheduled to land at Mzuzu Airport at 10:02 a.m.
The plane was unable to land at the airport due to poor visibility and was ordered to return to the capital, President Lazarus Chakwera said in a televised address to the nation.
"I'm holding on to every fibre of hope that we'll find survivors," he said, adding that the search area was concentrated around a 10 km (6 mile) radius in a forest reserve.
"I have given strict orders that the operation should continue until the plane is found."
He said Malawi had reached out to neighbouring countries, and the U.S., Britain, Norway and the Israeli governments for support in the rescue efforts.
Chilima, seen as a potential candidate in next year's presidential election, was arrested in 2022 over graft allegations.
However, a Malawi court dropped the corruption charges against him last month after the director of public prosecutions filed a notice for the case to be discontinued. Chilima has denied any wrongdoing.
