Johnson, who returned to the Texans' active roster for their Week 13 matchup against the Indianapolis Colts after missing three games because of a concussion, didn't practice Thursday due to what interim head coach Romeo Crennel called a "personal issue."
"So he had to deal with that," Crennel told reporters Friday morning. "We'll see how he's done with that."
League sources told the Houston Chronicle that Johnson is considered a close contact, leading to his placement on the COVID-19 list. The former Arizona Cardinals runner and his family are undergoing testing.
Texans backup running back Duke Johnson was limited in Thursday's practice with an illness but was a full participant Friday. He is expected to take over as the team's primary tailback against the Bears.
In nine games this season, David Johnson has recorded 452 yards and four touchdowns on 113 carries. The Texans acquired him as part of the blockbuster trade that sent Pro Bowl wide receiver DeAndre Hopkins to the Cardinals this past off-season.
Duke Johnson has 209 rushing yards and one score on 69 carries in 10 games this season. He filled in for David Johnson during his recent three-game absence.