Perozo, 29, who was a free agent after leaving first division club Zulia in December, was killed at a sports centre on Sunday morning along with Jaime Alberto Tey.
"According to the preliminary information, the two were involved in an argument with a man who opened fire," said the statement.
Venezuelan media said that incident happened outside a bar at the sports centre in the town of Lagunillas.
Zulia, the Venezuelan Football Federation (FVF) and the players' union (AUFPV) all issued statements offering their condolences. Perozo, a defender, had previously played for Carabobo FC.
"The professional footballers of Venezuela express their heartfelt condolences and repudiate the violence which affects the country and claims the lives of Venezuelans every day," said the AUFPV.
"We demand that the authorities clear up this crime which ended the life of a professional who will always be remembered in this country's football."
- Sports & Recreation
- Society & Culture
- Venezuelan Football Federation