"This situation is not the fault of the students," said Senate Republican leader Bob Huff of San Dimas.
The bill would allow students who have met all other graduation requirements to receive their diploma.
"We have a high school graduation requirement in place that no one can meet," added Sen. Carol Liu (D-La Canada-Flintridge).
The Senate voted 36-0 to approve a bill that, if signed by the governor would take effect immediately and exempt 12th graders this year from the requirement for passing the exit exam.
"We want to support our young people in moving forward with their lives," said Sen. Loni Hancock (D-Berkeley).