Zbigniew Ziobro, who is also Poland’s Prosecutor General, said the case involved a murder and attempted murder.
Polish website Onet.pl reported that the two men had their kidneys and other organs removed after travelling to Mexico earlier this month.
One of the men died and the other is in hospital.
"I have instructed the District Prosecutor's Office in Kraków [southern Poland] to investigate the murder of a young Pole in Mexico and the attempted murder of another countryman,” Ziobro wrote on Twitter.
He added: “The aim is to clarify all the circumstances of the case."
The foreign ministry in Warsaw said the condition of the man in hospital was improving.
It said inquiries were ongoing, adding: “We appeal to people not to speculate on this matter.”
The ministry told reporters that a Polish consul was in “constant contact” with the families of the two men and with Mexican prosecutors investigating the case.