In a statement, the foreign ministry said the case of Guadalupe Garcia de Rayos illustrated "the new reality".
The mother-of-two was detained on Wednesday when she went for a routine check-in with immigration officials.
President Donald Trump has promised to crack down on illegal immigrants with criminal records.
Garcia de Rayos, 36, had pleaded guilty in 2009 to using forged documents to get a job and was issued with a deportation order in 2013.