Mateo was arraigned on Sunday in New York on assault charges and released on $3,000 bail. Police contend that Mateo punched, bit and choked his wife, Aurea, during an argument early Saturday morning.
The pitcher was charged with third-degree assault, a class A misdemeanor, and is to return to court on June 15. The Mariners, meanwhile, suspended Mateo for 10 days, without pay, and replaced him on the 25-man roster with Sean Green.
Mateo returned to Seattle on Sunday and met with club officials on Monday.
"I am personally embarrassed by the incident on Saturday morning, which resulted in my arrest and absence from my team," Mateo said in the press release. "I recognize that I have also embarrassed my wife and family, my teammates and the entire Mariners organization in front of our fans."
Mateo is prohibited from going near his wife or contacting her.
"Without getting into detail, I understand that my behavior was inappropriate," he added in the statement. "I am very sorry for this, and want to apologize to all of them."
Mateo said he could not comment further, but has pledged to begin personal counseling immediately "to help address any issues that I may have. Beyond stating again my deepest regrets, I cannot comment further."
A 10-day suspension would cost Mateo almost $55,000 of his $1 million salary. He has two children and also supports his late brother's five children. His brother was killed in a traffic accident last year in the Dominican Republic.
Mariners president Chuck Armstrong said the organization "deplores domestic violence. There is simply no excuse for it."
The organization did not announce what would happen after the 10-day suspension ends. Mateo was optioned to Triple-A Tacoma on Saturday after the Mariners' game against the Yankees. He was suspended the next day for missing Saturday's game without the club's permission.