The Yucatan state prosecutors' office confirmed Tuesday that Arozarena was detained "for problems relating to his ex-partner.''
He has not been formally charged yet. On Wednesday, the case was referred to a judge in the city of Merida. The attorney general's office for Yucatan reported that Arozarena's legal process will continue before the corresponding court and a hearing is scheduled for Thursday, at which point a decision on potential charges could be made.
"We are aware of reports that Randy Arozarena was detained in Mexico," the Rays said in a brief statement Tuesday. "We are gathering more information on this situation, and we have no further comment at this time.''
Major League Baseball is likely to investigate under its joint domestic violence policy with the players' association.
"We are aware and looking into it,'' the commissioner's office said in a statement.
Arozarena, 25, has made no public comment, and it was not clear whether he had a lawyer yet.
Arozarena hit .377 with 10 homers and 14 RBIs in 20 postseason games for Tampa Bay. He was named MVP of the American League Championship Series.
The Associated Press contributed to this report.