Three armed men stormed into a nightclub called La Madame in the regional capital Xalapa yesterday morning, shooting four victims at a table inside.
"Four elderly men were killed," the state government said in a statement. Several more were injured, an official told AFP, without specifying a number.
Local media reported that the attack injured 12 people.
Xalapa, a city of 525,000 residents, lies 290 kilometers (180 miles) east of Mexico City near the Gulf of Mexico.
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The church was packed with families gathered for the confirmation of several children, including the daughter of the kidnapped man, whom officials named as Agustin Urena Estrada.
Security forces are working to find him, Veracruz Governor Javier Duarte tweeted.
Authorities believe he belongs to an organized criminal group and is nicknamed El Chango, security officials said.
Also yesterday morning, police killed another member of an organized criminal group during a clash in a bar in the city of Orizaba, south of Xalapa, the Veracruz government said in a separate statement.
The official who spoke to AFP declined to say whether a connection existed between the three incidents, but stated that investigations were under way.
Violence has skyrocketed in energy-rich Veracruz since 2010, when the ruthless Los Zetas drug cartel took control of criminal activities in the state, where it has waged a war on the news media, turning the region into one of the most dangerous for journalists.