Residents in the city that is home to the UN Human Rights Council and Red Cross will vote on Sunday on whether to allow authorities to impose fines of up to 100,000 francs ($110,000) on anyone who does not obtain permission to demonstrate and who does not abide by agreed conditions.
The cantonal government-backed amendments would also allow authorities to require changes to demonstration itineraries, if they posed "disproportionate risks to people" and their property, a move that would give officials the power to ban gatherings in the city centre.
"The exercise of fundamental freedoms should not be subject to a previous authorisation by the authorities," said Maina Kiai, the UN special rapporteur on the rights to freedom of peaceful assembly and of association.
The 100,000-franc potential fine was "disproportionate, and would have a chilling effect on the enjoyment of the rights to freedom of peaceful assembly and of expression," he added.
"Switzerland is leading important initiatives with respect to the promotion and protection of the right to freedom of peaceful assembly.
"The proposed changes to the law on demonstrations in the canton of Geneva are not in consonance with these positive efforts," he said.