The change also applies to volunteers, interns, contractors and vendors.
Indoor mask rules are also in effect inside the buildings.
The move comes amid the spread of the omicron variant, which has led to a record spike in COVID-19 cases in the last month.
The restrictions for visiting those institutions, housed at the Cultural Education Center in Albany, will take effect on Wednesday. It will apply to visitors age 5 and older.
The requirements for visitors are meant to match the rules in effect for visitors to the state capitol building, which put a similar policy in place this week. The Legislative Office Building has been closed to visitors.