Saulos Chilima and nine others were flying within the country on Monday morning when their aircraft disappeared from airport radars.
The plane, a military aircraft, was flying in bad weather.
Soldiers have been searching Chikangawa Forest in an effort to find the plane.
In press briefing on Tuesday, Malawi Defence Force commander Paul Valentino Phiri said fog has reduced visibility in the forest, thus complicating search efforts.
President Lazarus Chakwera has said the mission must continue until the plane is found.
He told Malawians in an address on Monday evening: “I know that we are all frightened and concerned – I too am concerned.
“But I want to assure you that I am sparing no available resource to find that plane and I am holding onto every fibre of hope that we will find survivors.”
However, Dr Chilima’s party, the United Transformation Movement (UTM), said they were “disappointed” with the search operation.
UTM officials alleged that the search started at 15:00 local time (14:00 GMT) despite the plane going missing at 10:00.
The vice-president and president come from different parties but the two teamed up to form an alliance during the 2020 elections.
Dr Chilima, 51, was on his way to represent the government at the burial of former government minister Ralph Kasambara, who died four days ago.
Former First Lady Shanil Dzimbiri was also on the flight, which took off from the capital, Lilongwe, on Monday morning.
It was meant to land at the airport in the northern city of Mzuzu, but was turned back because of poor visibility.
President Chakwera said he has contacted the governments of various countries, including the US, UK, Norway and Israel, who had all offered support “in different capacities” to help find the plane.
Dr Chilima has been vice-president of Malawi since 2014.
He is widely loved in Malawi, particularly among the youth, AFP news agency reports.
However, Dr Chilima was arrested and charged in 2022 on allegations that he accepted money in exchange for awarding government contracts.
Last month, the court dropped the charges, giving no reasons for the decision.
Dr Chilima is married with two children