Johnson suffered a knee injury in the first quarter of Thursday's 34-23 win over the visiting Baltimore Ravens and did not return to the game.
The Bengals also sustained an injury on the offensive line as rookie center Billy Price exited Thursday's game with what head coach Marvin Lewis termed a foot sprain during a media briefing on Friday, per the Cincinnati Enquirer.
Lewis did not offer a timetable for the return of either player, but said neither injury was considered season-ending.
The 6-foot-7, 280-pound Johnson was among the final cuts when Cincinnati trimmed its active roster to 53 players, but he was re-signed shortly afterward.
A member of the Bengals since he was selected in the third round of the 2009 NFL Draft, Johnson started at least 15 games in six of the past seven seasons.
Johnson had 49 tackles and five sacks in 2017, boosting his career total to 44 sacks in 140 games. Cincinnati has plenty of depth on the defensive line, including rookie Sam Hubbard along with Jordan Willis and Carl Lawson.
Price, who tore a pectoral muscle at the NFL Combine, was selected in the first round (No. 21 overall) of the 2018 NFL Draft. Lewis expressed surprise that he was not able to return even on an emergency basis Thursday.
The 6-foot-4, 305-pound Price started at guard for three seasons with Ohio State before shuffling to center in 2017.
Price was the 2017 Big Ten Rimington-Pace winner as the conference's top offensive lineman and Rimington Trophy winner as college football's top center. He finished his career with school records for both total and consecutive starts (55).