Christian Castro, 52, also faces state charges in the shooting.
Maria Alejandra Gomez-Quiroz is being held in Texas' Dilley detention center.
"He must face justice in Minnesota," Minnesota AG Keith Ellison said.
Oswaldo Pirela, the minor league catching coordinator for the Padres, was detained by ICE at the El Paso International Airport early Sunday.
Immigration and Customs Enforcement officers may soon be outfitted with gloves that can deliver painful electric shocks intended to gain compliance from combative individuals.