The minister of commerce and industry Rishath Bathiyutheen was accused of threatening the magistrate in the northeastern town of Mannar last week.
He has denied the accusation.
Bathiyutheen had verbally ordered the magistrate to revoke an earlier order in a case where his supporters were involved.
A mob of his supporters turned violent against the judge and hurled debris at the court causing damage to the building.
Last Friday, the judges and lawyers in joint action stayed away from courts throughout the island in protest against Bathiyutheen.
The lawyers who petitioned the appeal court said that Bathiyutheen had undermined the independence of the judiciary.
He should be asked to show cause why he should not be charged for contempt of court, they said.