The department began scanning and retaining documents, such as birth certificates and concealed weapons endorsements, as part of the new licensing procedures in December.
Tuesday's 29-5 vote came just a few hours after Gov. Jay Nixon announced the department would stop scanning the concealed weapons permits. Republican lawmakers have raised concerns that the documents held in a state computer system are an invasion of privacy.
Democratic Sen. Jamilah Nasheed, of St. Louis, called the bill "pathetic" and criticized Republicans for spending time on the license controversy.
The measure would also require county sheriffs to issue concealed weapons licenses, instead of the Revenue Department.
The driver's license bill is SB252.