Horowitz was in the midst of the 11th day of hearings on the grievance filed by the players' association to overturn the 211-game suspension given to Rodriguez by Major League Baseball last summer for alleged violations of the sport's drug agreement and labor contract.
"I'm done. I don't have a chance. You let the arbiter decide whatever he decides," Rodriguez said during an interview on WFAN radio. "My position doesn't change. I didn't do it."
A person familiar with the session said that after Horowitz made his ruling, the New York Yankees third baseman slammed a table, uttered a profanity at MLB Chief Operating Officer Rob Manfred and left. The person spoke on condition of anonymity because what takes place at the hearing is supposed to be confidential.
"I am disgusted with this abusive process, designed to ensure that the player fails," Rodriguez said in a statement. "I have sat through 10 days of testimony by felons and liars, sitting quietly through every minute, trying to respect the league and the process.
"This morning, after Bud Selig refused to come in and testify about his rationale for the unprecedented and totally baseless punishment he hit me with, the arbitrator selected by MLB and the players' association refused to order Selig to come in and face me. The absurdity and injustice just became too much. I walked out and will not participate any further in this farce."
Rodriguez's legal team remains involved in the proceeding. Rodriguez said he had planned to testify later this week but was warned by the union he could face additional discipline if he did.
In a lengthy interview on WFAN, Rodriguez said he consulted Biogenesis of America head Anthony Bosch for "nutrition and weight loss."
Rodriguez repeatedly denied using PEDs during the period in question and said Selig "hates my guts," is "trying to destroy me" and "doesn't have the nerve to come and face me face to face."
Horowitz technically is chairman of a three-man arbitration panel that also includes Manfred and Dave Prouty, the general counsel of the players' union.
"For more than 40 years, Major League Baseball and the players' association have had a contractual grievance process to address disputes between the two parties. This negotiated process has served players and clubs well," the commissioner's office said in a statement. "Despite Mr. Rodriguez being upset with one of the arbitration panel's rulings today, Major League Baseball remains committed to this process and to a fair resolution of the pending dispute."
Selig testified in 2000 on the rationale of his decision to suspend Atlanta pitcher John Rocker for all 45 days of spring training and the first 28 days of the season, a penalty cut to the first 14 days of the regular season by arbitrator George Nicolau. Selig also testified in the 2002 contraction grievance, which settled.
Among other baseball commissioners to testify were Bowie Kuhn in the 1980 Ferguson Jenkins case, Peter Ueberroth in the 1980s collusion proceedings and Fay Vincent in the 1992 Steve Howe arbitration.
"The MLBPA believes that every player has the right under our arbitration process to directly confront his accuser," the union said in a statement. "We argued strenuously to the arbitrator in Alex's case that the commissioner should be required to appear and testify. While we respectfully disagree with the arbitrator's ruling, we will abide by it as we continue to vigorously challenge Alex's suspension within the context of this hearing."
The three-time AL MVP said four years ago he used PEDs while with the Texas Rangers from 2001-03, but has denied using them since. At the time of his suspension, MLB said the penalty was for "use and possession of numerous forms of prohibited performance-enhancing substances, including testosterone and human growth hormone over the course of multiple years" and for "engaging in a course of conduct intended to obstruct and frustrate the office of the commissioner's investigation."