The Fox News anchor sat in relatively close proximity to Trump at the debate, during which neither Wallace nor the participants wore masks.
Biden, according to campaign officials, last tested negative for COVID-19 on Sunday, with two negative tests on Friday.
Health officials recommend waiting around 5 to 7 days from a potential exposure to get a COVID-19 test in order to prevent false positives.
Trump, after undergoing treatment at the Walter Reed medical facility in Maryland, returned to the White House on Monday after a three-day stay.
“Don’t be afraid of Covid. Don’t let it dominate your life. We have developed, under the Trump Administration, some really great drugs & knowledge. I feel better than I did 20 years ago!” Trump wrote in a tweet as he was preparing to leave the hospital.
In a video Monday night, Trump doubled down on the message that the illness, while serious, can be beaten, saying, “Be careful,” but “don't let it dominate you.”
“You’re going to beat it," he said. "We have the best medical equipment, we have the best medicines.”
A number of the president's close associates have recently tested positive for the CCP virus, including White House aide Hope Hicks, Trump campaign manager Bill Stepien, Republican National Committee chairwoman Ronna McDaniel, and White House press secretary Kayleigh McEnany.
While the White House has not insisted on wearing facial coverings as a safety measure against the virus, it has in place a rigorous testing regimen. The president is tested regularly, as are his most senior aides, and anyone in close proximity to Trump or Vice President Mike Pence is tested prior to the day's events, including reporters.