Carr cited health reasons in his resignation letter to the board of supervisors Monday.
A special election to fill the remainder of the term is scheduled for Nov. 4. The job pays $47,844 annually.
Supervisors appointed Tupelo attorney Dennis Voge to serve as interim judge beginning June 1.
Carr has served as a judge for 24 years. He had been re-elected to a term that began in January 2012. The term ends in January 2016.
Justice court judges and other elected county offices with four-year terms will appear on the ballot in 2015. Educational requirements for justice court judge don’t include a law degree, only a high school diploma.