According to Schefter, Jackson is dealing with cold-like symptoms, but is expected to make a full recovery.
Mike Klis adds that he spoke to Jackson, who said he started feeling congestion two days ago and then experienced some chills.
The plan is for Jackson to be quarantine for the next two weeks.
Broncos OLB Von Miller previously tested positive for the virus back in April, but has since been cleared.
Jackson, 32, is a former first-round pick of the Texans back in 2010. He played out the final year of his four-year, $34 million contract before agreeing to a three-year, $33 million contract with the Broncos last year.
In 2019, Jackson appeared in 13 games for the Broncos and recorded 71 tackles, two interceptions, a forced fumble and 10 pass defenses.