The soldiers vanished Saturday in Massachusetts where they were participating in a military training exercise at Joint Base Cape Cod.
U.S. Immigration and Customs Enforcement said in a statement that the officers face removal proceedings after being charged with administrative immigration violations.
A spokesman for ICE said the agency cannot provide more details on the charges or say where the men were being held.
The Massachusetts National Guard said earlier that the Afghan soldiers, identified as Maj. Jan Mohammad Arash, Capt. Mohammad Nasir Askarzada and Capt. Noorullah Aminyar, had been detained by the Canada Border Services Agency on Monday.
U.S. authorities have said that they do not believe the men posed any danger to the public.
Massachusetts Gov. Deval Patrick said on Monday that the soldiers had been fully vetted before entering the U.S., adding there was speculation within the military that they might be seeking to defect.