While homosexuality is extremely taboo in Liberia, and voluntary sodomy considered a criminal offence, the question of gay marriage had not been expressly addressed in law.
The amendment was made to section 2.3 of the constitution, which bans marriage between those who are already married and close family members. It adds "or persons of the same sex" to the text, as read by the chairman of the judiciary committee, Joseph Nagbe.
The bill was sponsored by Senator Jewell Taylor, ex-wife of former president Charles Taylor, who in May was sentenced to 50 years in prison for war crimes and crimes against humanity.
"My bill seeks to ensure that the fact that people of the same sex under our law should not be allowed to get married," Taylor said.
The bill will be sent to President Ellen Johnson Sirleaf, who has the final say on whether it becomes law.
A second bill which seeks to make sexual relations between two people of the same sex a first-degree felony is currently before the House of Representatives.
The legislation comes after an acrimonious public debate on gay rights after a group of activists earlier this year began lobbying for a bill legalising same-sex marriage.
The leaders of the Movement in Defence of Gay and Lesbian Rights -- none of them gay themselves -- were mobbed and had to be rescued by police when they tried to campaign at a university campus.
This created a furore in the country and posed a thorny issue for Sirleaf, a Nobel Peace Prize winner who has approached the issue of gay rights uncomfortably.