The local government issued the warning in response to mounting pressure from some political parties.
Zurich cantonal police have announced their intention to charge protesters for such acts but their city colleagues are against the idea. Both forces operate independently of each other.
There have been several roadblock protests in Switzerland but mainly in the western French-speaking part of the country.
In October, climate activists temporarily blocked the Mont Blanc Bridge in Geneva when they glued their hands to the asphalt.
There has only been one road blocking protest recorded in Zurich recently, which caused less obstruction than others in different parts of the country.
Nevertheless, the Zurich youth section of the rightwing People’s Party is gathering signatures in an effort to force a public vote on charging protesters.
Solidaritätsnetz International asks non-governmental organizations to refrain from escalating mutual hatred and jointly seek compromises.