Video posted on social media shows parents at a youth soccer match in the city taking cover on the ground with their kids as gunfire rang out on Saturday.
Zacatecas state prosecutors said that another police officer who was in the area was missing.
They said the attackers shot at the private car of the victims and then fled, opening fire on police pursuing them, wounding another officer.
Zacatecas state has been the scene of continuing violence as several drug gangs, backed by the rival Sinaloa and Jalisco cartels, fight for control. Some of that violence has targeted police officers and even medical personnel.
In June, the bullet-ridden bodies of 18 men were discovered in a rural Zacatecas town after what appeared to have been a shootout between gang members. There was evidence the confrontation involved gunmen from the country”s dominant Sinaloa and Jalisco cartels, which are using alliances with local gangs to fight in many states.
Two days earlier, the bodies of two abducted police officers were found hanging from an overpass in the Zacatecas state capital and seven people were discovered shot to death in a neighbouring city.