The resolution would eliminate the Independent Redistricting Commission.
Voters approved an initiative in 2000 creating the five-member commission and making it responsible for the once-a-decade redrawing of new congressional and legislative districts.
The Senate measure would be subject to voter approval in November because it amends the state Constitution.
Republican legislators have accused the commission of violating constitutional criteria for the redistricting process.
The Senate proposal was approved Thursday by a 21-9 vote along party lines, with Republicans in support. It now goes to the House.