Senate Bill 2095 would allow a person with a marijuana prescription to obtain up to 3.5 grams of the substance per day. The bill also sets taxes on the production and sale of cannabis, and it specifies that plants must be grown indoors under controlled conditions.
Republican Gov. Tate Reeves has said that amount is too large, and he believes it would lead to widespread recreational use of the drug. He wants legislators to revise the bill.
A voter approved initiative was struck down last year by the Mississippi Supreme Court.
After the court ruling, a Republican-led group of legislators spent months negotiating to create a medical marijuana program with the hope that Reeves would call the House and Senate into special session to put it into law during the fall. Reeves never called a special session.
The bill passed the 52-member Senate on Thursday with strong bipartisan support. Only five senators voted against it. House leaders have not said how soon that chamber could vote.
The Associated Press contributed to this report.