World number one Nadal picked up his back injury during the Australian Open final which he lost to Swiss Stanislas Wawrinka.
Nadal posted a video apologising to fans for not being able to make the event in Argentina.
He said a recent stomach virus meant he could not practice and was therefore not ready to play in the clay court event.
He is still scheduled to play in Rio de Janeiro, also on clay, later this month before the competing in the hardcourt Masters events at Indian Wells and Miami.
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