Christian Castro, 52, also faces state charges in the shooting.
A Cary woman and permanent U.S. resident is being held in immigration detention in Georgia after what her family believed would be a routine check-in.
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.