In a tweet on Monday, Carlos Slim Domit wrote that his 80-year-old father began having minor symptoms a week ago and sought care at one of the country's foremost hospitals.
Slim's family owns Mexico's largest telecommunications provider.
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Word of the elder Slim's hospitalization came days after Mexico's leader, President Andrés Manuel López Obrador, said he himself had tested positive for the coronavirus.
On Sunday, López Obrador announced via Twitter that he had tested positive, had mild symptoms and was undergoing treatment. Since then he has been out of the public eye with the exception of a photo circulated on his Twitter account Monday showing him sitting stiffly behind a desk in jacket and tie.
The Associated Press contributed to this report.