"Professor Peter Mutharika has the right to hold or campaign for any position in this country just like anybody else. He can stand for any position. I mean any position," the president was quoted by state radio as saying.
Mutharika appointed his brother, who is an MP in the president's Democratic Progressive Party, as justice and constitutional minister after a winning re-election in May.
Peter Mutharika, a former professor of international law at a US university, was also previously advisor on law and justice matters to the president.
The president said his brother will not be "stopped from pursuing his ambitions just because he is my relation. Is it an offence to be a brother of the president?"
Mutharika said he will not nominate anyone to succeed him, but the "system will elect my successor on its own. It will be up to Malawians to choose who they want."
Mutharika, who will be 80 by the time he is due to step down, is not allowed to run for a third term under the constitution and has in any case said he would not wish to.
"I will not even extend my stay in State House by more than a day the moment the country elects another leader."