Cavazos had been forced from his home by armed men wearing out-of-date federal police uniforms on Sunday.
His bodyguard, the only witness to the abduction, was later found bruised but otherwise unhurt, locked in the boot of a car.
Felipe Calderon, the president, who has staked his reputation on tackling the drug cartels, condemned the "cowardly assassination."
"The murder of Edelmiro is an outrage and forces us to redouble our efforts to fight these cowardly criminals," Calderon wrote in an update on the microblogging service Twitter.
Santiago has become a staging post for drug gangs smuggling narcotics north into the United States.
The town is at the outskirts of the city of Monterrey, where drug violence has surged as a dispute between the powerful Gulf cartel and its former armed wing, the Zetas, turned into all-out war since the start of this year.
Leading local business groups published a full-page statement in Mexican newspapers on Wednesday urging Calderon to send more troops to Monterrey and called on local, state and the federal government to stop blaming one another for the violence and do more to stop it.
More than 28,000 people have died in suspected drug violence since the end of 2006, when Calderon launched a controversial military crackdown on organised crime.