The Senate gave the measure preliminary approval Friday. That puts the Senate on track to vote on the bill Monday, the last day of the legislative session.
The bill would create a state commission to oversee medical marijuana programs at academic medical research centers that decide to participate.
The House of Delegates already has approved the bill.
Maryland's health secretary has expressed support for the measure. Last year, Secretary Joshua Sharfstein opposed it due to concerns the federal government could prosecute state employees. This year, the bill was changed to enable the governor to suspend the program if it is determined employees could be prosecuted for participating.