Colonel Maximo Aybar Baez, a spokesman for the Dominican police, said on his Twitter account that Carmona, whose actual name is Roberto Hernandez Heredia, was arrested after leaving the U.S. Consulate in the Dominican Republic on Thursday.
Authorities said Heredia is 31 years old and not 28, as he has claimed.
"This arrest is part of the measures taken by the National Police (NP), in coordination with the American Consulate. The NP invited Dominican prospects not to be misled by those who sell fake illusions based on illegality," Baez said on Twitter.
The pitcher was trying to renew his visa so he could attend spring training in February.
The arrest is the second identity case involving a major leaguer in four months. Last fall, police in the Dominican Republic arrested Miami Marlins pitcher Leo Nunez for using a false identity. He is actually Juan Oviedo and he remains on the Marlins' roster.
Oviedo, who no longer faces charges, agreed to a one-year, $6 million contract with the Marlins earlier this week, but his visa status remains uncertain.