"Even demonstrations intended to be peaceful can turn confrontational and escalate into violence. You should avoid areas of demonstrations, and exercise caution if in the vicinity of any large gatherings, protests, or demonstrations. Be alert and aware of your surroundings," the embassy said.
Police and organizers expect a large number of participants and traffic congestion may be heavy in the city centre around the time of the demonstration, it added.
The embassy recommended that US citizens traveling to or residing in Croatia register with the Embassy Zagreb for the latest security updates and to make it easier for the embassy to contact them in an emergency.
The US Embassy issued similar warnings ahead of a recent game between Croatian and Serbian football teams in Zagreb and last year ahead of Pride parades in Split and Zagreb.
The Committee for the Defense of Croatian Vukovar will organize a rally at noon on Sunday in Ban Jelacic Square in downtown Zagreb, protesting against the introduction of Cyrillic signs in the eastern town of Vukovar and throughout Croatia. Committee president Tomislav Josic has said he expects the square to be full of Croatian patriots and all those who support what the Committee advocates and seeks.