"I ask for the forgiveness of my fans, the government of the United States and the Cleveland Indians for this situation," he said upon leaving the court, where a judge released him on bail of about $13,000.
Police arrested him Thursday outside the U.S. consulate in his native Dominican Republic when he arrived to get his visa renewed. Spokesman Maximo Baez Aybar said the athlete's real name is Roberto Hernandez Heredia and that he is 31, three years older than he had claimed.
He was the second Dominican player arrested in recent months for using a false identity.
Marlins reliever Leo Nunez was arrested last month for using a false identity, three months after the team placed him on the restricted list when it became known he was playing under an assumed name.
Nunez, whose actual name is Juan Oviedo, was quickly released and officials said he would not be prosecuted because he was cooperating with a larger investigation into the use of false documents.
Lawyers for Hernandez said the Indians pitcher would speak in more detail at a later news conference. Judge Keyla Perez ordered him not to leave the country and required him to check in with prosecutors while the case is under further investigation.
His lawyer, Joaquin Perez, said they did not know if pther players were also under investigation in the case.
Carmona is due to make $7 million this year, and the Indians hold options for 2013 at $9 million and 2014 at $12 million.
"We were recently made aware of the situation that occurred today in the Dominican Republic and are currently in the process of gathering information," general manager Chris Antonetti said after the arrest.
Carmona's career in Cleveland has been one of extremes.
After going 1-10 in 2006, the right-hander with a wicked slider won 19 games in 2007, shocking the Indians, who had briefly experimented with him as a closer. Carmona 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 went just 7-15 last season, Carmona stayed healthy, didn't miss a start and was expected to be part of the starting rotation this season.