Burrow, regarded as one of the most talented quarterbacks in the NFL, suffered torn ligaments in his wrist in Thursday's 34-20 loss to the Ravens.
Burrow told reporters on Friday he had felt a "pop" in his wrist in the second quarter and had hoped to continue but was unable to.
The Bengals confirmed on Friday that Burrow was out for the remainder of the season.
"It's tough," Burrow said. "You work so hard for seasons and moments like these so whenever you get hurt and it ends it early, it's tough to handle."
Burrow, 26, was chosen by the Bengals with the top pick in the 2020 NFL draft and has helped revive the team's fortunes.
He suffered a knee injury that cut short his rookie season in 2020 but returned the next season to lead the Bengals to the Super Bowl, where they lost to the Los Angeles Rams.
"It's part of the game," Burrow said of his injury. "I've been through it before, so just got to grind it out."
Burrow's injury leaves the Bengals in a daunting position.
They are 5-5 at the bottom of the AFC North and have little margin for error if they are to mount a late charge for the playoffs.
The two teams above them, Pittsburgh and Cleveland, are 6-3. Baltimore lead the division with an 8-3 record.
Bengals coach Zac Taylor insisted there was no chance of Cincinnati throwing in the towel.
"The season is far from over," Taylor said Friday.
