The lawsuit, filed in U.S. District Court in Jackson, said the supervisors can't redraw the districts and get federal government approval before Tuesday's qualifying deadline for candidates for county offices.
Madison County's population grew by about 20,000 people in the last 10 years, according to the 2010 census.
The lawsuit said some of the county's districts grew more than others, so redistricting is required.
Madison County resident and attorney John W. Robinson, III, is also a plaintiff in the suit.
The state, Madison County Circuit Clerk Lee Westbrook and the local Republican and Democratic executive committees are named as defendants.
The extension of the filing deadline may be something many counties need, because not much time was available from the time 2010 Census data was received and the Mar. 1 candidate qualifying deadline.
Mississippi's district lines have to be approved by the U.S. Department of Justice.