The sacking was part of the shake-up of top officials unveiled by President Banda Tuesday.
Ms Banda also purged Mutharika loyalists in charge of government finances and media.
“Although we are in mourning, certain decisions cannot wait,” President Banda told a news conference in the capital Lilongwe, three days after taking office.
She also announced an investigation into the mysterious murder of student activist Robert Chasowa.
Mr Mutharika’s critics have accused police of staging a hit against Mr Chasowa, implicating former police chief Peter Mukhito, who was sacked on Monday.
“As a mother, I feel for my fellow mother who doesn’t know what killed her son. I understand how painful it is, and I will make sure we find out who killed our son Chasowa,” President Banda said.
“We don’t want people to go about murdering people fearlessly.”
Top among Banda’s new appointments was Mary Nkosi as Reserve Bank Governor, making her the first woman to hold the job.
A long-time deputy governor, she replaces Mr Perks Ligoya, a close ally of Mutharika who pursued a rigid exchange rate policy that the International Monetary Fund has blamed for much of Malawi’s economic woes.
She named a new secretary to the Treasury, appointing career bureaucrat Radson Mwadiwa, who also becomes chairman of the state-owned Malawi Savings Bank.
The new Information minister is Mr Moses Kunkuyu, a parliamentarian who broke away from Mutharika’s Democratic Progressive Party to press for reforms.
The President Banda also sacked the head of the Malawi Broadcasting Corporation, Mr Bright Malopa, another Mutharika ally who used state media to campaign against Banda after her expulsion from the DPP.
The new director general is Mr Benson Tembo, a veteran broadcaster and former diplomat whose last posting was as ambassador to Zimbabwe.
Meanwhile, Liberian President Ellen Johnson Sirleaf has welcomed Ms Banda as the second woman leader in Africa.
The continent’s first woman president said her ‘loneliness’ was over with the coming of Ms Banda, who she offered some advice as she occupies the top seat.
“This means I no longer will be lonely. The potential for more women leadership at the highest level is now being made even stronger,” she said.
In an interview with the BBC on Monday, President Sirleaf narrated how being the only woman leader among over 50 of her colleagues had been discomforting for her.
But she also had words of caution in terms of her relationship with her government and beyond.
“She will have some difficulties; there will be some male leaders that will not accept her fully,” said President Sirleaf.
“But I think once she sets that example, it will not be difficult for them to accept and to work with her.”