Governor Doug Ducey said he heeded the advice of the state's police chiefs who opposed the bill.
They had argued that the lack of transparency would hinder police-community relations.
But police unions pushed for the bill, saying the 60-day delay would ensure officer safety.
Legislatures across the US are taking up various pieces of police-related legislation after the shooting of a black teenager in Ferguson, Missouri, last August sparked weeks of protests.
Other states are considering proposals requiring police to wear body cameras or mandating that shooting investigations be done by outside agencies.
However, Arizona was the only state considering restricting information about officers in involved in shootings.
In a letter explaining his veto, Ducey said he sympathized with the bill's supporters but said there were other ways to keep officers safe.
Tucson Police Chief Roberto Villasenor, who is also president of the Arizona Association of Chiefs of Police, said the bill would have worsened already poor police-community relations after the events of Ferguson.
"Enacting legislation that would hamper that trust by not allowing officers' names to be released is not in my opinion the best way to improve or repair that level of trust," Villasenor said.
The governor of Arizona has vetoed a bill that would have kept the names of police officers involved in shootings secret for 60 days.