Organisers say the self-rule envisioned for Kosovo's Serb minority could lead to the creation of a separate Serb entity within Kosovo.
Activists also rejected parts of the plan that call for the establishment of a new international mission that would have powers to annul decisions or laws that run against the plan itself.
The group also criticised ethnic Albanian leaders for negotiating with Serbia. Talks between the two sides are to resume February 21.
Tear gas
Barnaby Phillips, Al Jazeera's correspondent in Pristina, said that many people were hospitalised after protesters waving sticks tried to break through a police barricade and were met with tear gas, one of which struck a protester in the stomach.
Martti Ahtisaari, chief UN envoy, unveiled his proposal for Kosovo's future status a week ago.
The plan does not explicitly call for Kosovo's independence from Serbia, but spells out conditions for self-rule - including a flag, anthem, army and constitution, and the right to apply for membership in international organisations.
Kosovo's Serb minority would have a high degree of control over their own affairs.
The plan, which needs approval from UN Security Council to come into force, was endorsed by Kosovo's ethnic Albanian leaders but rejected by Serbian officials in Belgrade who refuse to give up the province, considered Serbia's historic heartland.