The amendment, put forward by Prime Minister Kyriakos Mitsotakis, would allow visitors but prohibit demonstrations, with penalties including fines or imprisonment for violators.
Opposition parties have strongly criticised the proposal, deeming it unconstitutional and an attempt to curtail freedom of expression and protest.
The monument has been a focal point for public demonstrations, notably by relatives of the 57 victims of the February 2023 Tempi train crash, who have set up a makeshift memorial there.
While the government states the aim is to respect a sacred national monument, critics argue the move is a direct response to anti-government protests following the train disaster.