The 24-year-old had the tattoo inked on his arm on Monday and it subsequently became inflamed, ruling him out of Saturday's final against Borussia Dortmund.
Frankfurt's director of sport Fredi Bobic told the club's official website: "This behaviour is grossly negligent and hurts the entire team.
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"Guillermo's path with Eintracht is over following this action. The club cannot tolerate a player defying the coach and doctors before such an important game.
"We had already thought about a possible extension of the loan. This is no longer a matter of course.
"Guillermo is suspended with immediate effect."
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