The 28-year-old Venezuelan ace, a back-to-back All-Star, was taken into custody after agents raided his apartment in Pittsburgh, the Florida Department of Law Enforcement said.
Vazquez has been charged with one count of computer pornography, solicitation of a child and one count of providing obscene material to minors.
Law enforcement said the arrest followed the opening of an investigation in August after agents obtained information that Vazquez had a sexual relationship with a 13-year-old female.
The victim, who is now 15, had continued to have a relationship with Vazquez via text messaging.
In July, Vazquez sent the girl a video which showed him performing a sex act, police said.
Vazquez had also sent messages suggesting the two would meet for sex when the baseball season was over, Florida officials added.
Police seized several electronic devices as part of the investigation. Vazquez will be extradited to Florida to face prosecution.
The Pirates meanwhile said Vazquez had been placed on leave by Major League Baseball following the revelations.