The arrest comes days before the court is expected to deliver its ruling on the election petition mounted by the opposition.
The Anti-Corruption Bureau (ACB) said it had arrested Thomson Mpinganjira, owner of FDH Bank, following investigations into claims by Chief Justice Andrew Nyirenda that bribes had been offered to the five judges presiding over the case.
"Mpinganjira will be taken to court after the ACB has recorded a statement from him," the agency said in a statement, without further details.
The aid-dependant southern African state has been embroiled in a battle over the credibility of the May 2019 election.
Mutharika won a second term, but his victory unleashed a six-month-long court case and nationwide demonstrations demanding the head of the electoral commission be fired.
Mutharika beat opposition candidate Lazarus Chakwera by 159,000 votes -- a lead of just over three percentage points.
Chakwera's Malawi Congress Party and the United Transformation Movement say the poll was marred by fraud.
Allegations this month by Chief Justice Nyirenda that the judges in the petition case had been offered kickbacks sparked fresh fury.
Tens of thousands of protesters marched last week calling for the culprits to be unmasked.
The Constitutional Court is expected to rule on the election challenge sometime between January 27 and February 3, its spokeswoman Agnes Patemba told AFP on Wednesday.
It is the first time presidential election results have been challenged in court since Malawi gained independence from Britain in 1964.
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