The tag for offensive linemen was set at $16.662 million, the league told teams Monday, according to a memo obtained by ESPN.
The deadline for teams to designate franchise players is Tuesday at 4 p.m. ET.
The Chiefs and Brown have until July 15 to agree to a long-term contract or he will play the 2022 season on his franchise tender.
Brown joined the Chiefs last year in a trade with the Baltimore Ravens and started 16 of Kansas City's regular-season games along with three postseason contests at left tackle. He was selected to the Pro Bowl for the third time in his career.
Brown, whose father, Orlando, was a longtime NFL offensive tackle, was a third-round draft pick by the Ravens in 2018. In three seasons with Baltimore, he started 52 games in the regular season and playoffs, mostly at right tackle.
Brown wanted to play left tackle, but that position with the Ravens was occupied by Ronnie Stanley, so he asked for a trade to a team that would play him at left tackle.
The Chiefs acquired Brown shortly before last year's draft and gave up four picks, including their 2021 first-rounder.
ESPN's Adam Teicher contributed to this report.