Argentina Football Association (AFA) vice president Claudio Tapia said the theft took place when Mexico and the South American team played to a 0-0 draw in the central city of Puebla on Thursday night.
It was the last preparation game before both countries compete in the Olympics in Rio de Janeiro, which start next Friday.
Small Olympic Village fire forces Australia evacuation
"When we returned at 11:40 pm and went up to the rooms, we realized that they had been robbed," Tapia said, without specifying how much money was taken.
The Mexican Football Federation said in a statement late on Friday that an agreement was finally reached between the AFA, the Camino Real hotel and an insurance firm to compensate the Argentine delegation.
Tapia said earlier that the team had given several statements to the authorities and complained of a "total lack of respect" in the way the issue was handled.
Olympics shambles: Rio marred by further controversy
He had warned that the delegation would not leave the hotel until it received guarantees that it would be compensated.
"You know what's the strangest thing? It's that they have verified and know who is the thief from the (security) cameras, so they are protecting the thief," he said before the Mexican football federation announced the agreement.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ