The Senate voted unanimously Tuesday to pass it.
The bill would allow only the use of cannabidiol, an oil extract, to be administered under the care of a doctor.
The Assembly approved the bill last week on a voice vote. It now goes to Gov. Scott Walker.
He has not said whether he will sign the bill should it pass.
The measure falls far short of legalizing the use of marijuana for medical purposes, something the Republican-controlled Legislature has shown no interest in pursuing.