The Mexican prosecutor general's office said the man was the target of an Interpol "blue notice," issued because the US Federal Bureau of Investigation (FBI) suspects him of "publishing support for violent jihad and radical Islam" online.
Interpol blue notices are issued "to collect additional information about a person's identity, location or activities in relation to a crime," according to the international police organization.
Mexican media reports named the man as Mohammed Azharuddin Chhipa.
He was arrested at a migrant detention center in the town of Huehuetan, in the southern state of Chiapas, near the Mexican-Guatemalan border, the federal prosecutor's office said in a statement.
Such centers are used to temporarily house undocumented migrants as Mexican immigration authorities process their cases.
The man was subjected to a hearing at the detention center and deported by plane to Washington on Friday, the prosecutor's office said.