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. The Indians list Carmona's birthday as Dec. 7, 1983, in their 2011 media guide.
"We were recently made aware of the situation that occurred today in the Dominican Republic and are currently in the process of gathering information," Indians general manager Chris Antonetti said. "We are not prepared to make any additional comment at this time."
The pitcher was trying to renew his visa so he could attend spring training in Goodyear, Ariz., next month.
Carmona was granted bail by a Dominican Court on Friday. After paying a $14,000 bond, he apologized to Dominican and U.S. authorities and announced that he would soon hold a news conference to give his version of the facts.
Due to the fact that this a case of identity fraud, Carmona no longer has a passport and must restart a process with the authorities in order to be able to travel outside of the Dominican Republic.
Carmona's agent said he was caught off-guard by the arrest and that there are Dominican lawyers working on the player's behalf. He did not disclose the names of the lawyers.
"This took us by complete surprise," agent Jay Alou said. "What we have to do now is wait to find out the process that has to be done with the consulate with this new identity in order to see if he can get a new work visa."
"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.
Carmona was the Indians' Opening Day starter last season. The right-hander finished 7-15 with a 5.25 ERA in 32 starts, and the club picked up his $7 million option for 2012 in October.
Carmona's career in Cleveland has included extreme highs and lows.
After going 1-10 in 2006, he came out of nowhere to win 19 games for Cleveland in 2007, shocking the Indians, who had briefly experimented with him as a closer. Carmona, though, followed up with a disappointing 2008 season, and in 2009 the club sent him to the lower minors to work on his mechanics.
Carmona rebounded to win 13 games in 2010, in manager Manny Acta's first season. Although he didn't have a winning record last season, Carmona stayed healthy, didn't miss a start and was expected to be part of the starting rotation this season. He has been pitching winter ball in the Dominican.
The Indians signed Carmona to a four-year contract in 2008. The club has options on him for 2013 at $9 million and 2014 at $12 million.
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.
Enrique Rojas is a reporter and columnist for ESPNdeportesLosAngeles.com and ESPN.com. Information from The Associated Press was used in this report.