A state police officer was wounded in the clash, a Veracruz public security agency official told AFP.
The skirmish erupted after security forces were shot at from a house as they searched for a kidnapping gang while driving down an avenue in the city of Perote, the agency said in a statement.
"As a result of this clash, nine men and one woman were killed," the statement said.
The authorities said the suspects were part of a Zetas unit dedicated to kidnapping and one of the cartel's most dangerous cells.
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Founded by a former elite military troops, the Zetas are known as a vicious gang blamed for much of the violence that has plagued Mexico in recent years.
But authorities believe the Zetas have been weakened following blows to their leadership in the past two years.
Zetas kingpin Miguel Angel Trevino was captured in the northeastern border state of Tamaulipas in July 2013, while his predecessor, Heriberto Lazcano, was killed in a shootout with troops in October 2012.
While officials say that murders have dropped in the past year in Mexico, where tens of thousands have been killed in drug violence, the number of kidnappings and extortion rackets have soared.
Federal officials say kidnappings and extortion have increased because authorities have had success against the drug cartels, forcing them to branch out.
More than 1,700 kidnappings were reported last year, up from 1,414 in 2012, according to federal statistics.
Three quarters of the kidnappings have taken place in 10 states, including Veracruz. Mexico counts 31 states plus Mexico City.
National Anti-Kidnapping Coordinator Renato Sales told a news conference yesterday that organised crime groups have been "dispersed," causing them to "migrate" from drug trafficking to other illegal activities such as kidnappings for small ransoms.