MLB Commissioner Rob Manfred said in a statement that the suspension was made following an investigation and that Cordero will participate in a confidential and comprehensive evaluation and treatment program supervised by the Joint Policy Board.
In a separate statement the Yankees said they are "fully supportive" on MLB's investigative process and the disciplinary action applied to Cordero.
The Yankees did not immediately reply when asked to provide a comment from Cordero.
Cordero was 3-2 with a 3.86 ERA in 31 appearances for the Yankees in 2023.
Cordero, who signed a Minor League deal with the Yankees in 2022 when he was recovering from Tommy John surgery, has also played for the Washington Nationals, Toronto Blue Jays and Chicago White Sox in his MLB career.