Willard, 56, is the latest high-profile person to get the virus in a global pandemic that has infected more than 245,000 people and killed over 10,000 globally.
Chief Financial Officer William Gifford Jr will take over for Willard during his absence, the company said in a memo to employees.
Altria said on Thursday it would temporarily suspend operations at a manufacturing facility in Richmond, Virginia, after a second employee tested positive for the virus.
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The outbreak has upended the lives of millions and has led to many companies around the world to effectively grind to a standstill.
People over the age of sixty-five are most vulnerable to becoming severely ill because of the virus, according to the U.S. Centers for Disease Control and Prevention.
(Reporting by Uday Sampath in Bengaluru; Editing by Bernard Orr)