The hacker movement known as "Anonymous Mexico" has posted a statement condemning "the bad government" on the press section of Mexico's Defense Department website.
The statement signed by group appeared on the press link for the site.
The statement includes a video showing street protests on December 1, when police cracked down on anti-government demonstrators.
The Defense Department issued a statement on Wednesday when the hacking began, saying its website was "temporarily out of service."
The department said no internal computer networks or information had been affected.