Drew Rosenhaus, Brown's agent, told Adam Schefter of ESPN that Brown was dealing with a "personal matter" and that he has spoken to the Steelers about it.
Ed Bouchette and Gerry Dulac of the Pittsburgh Post-Gazette first reported the news of Brown's absence for meetings and film study.
Pittsburgh is now 0-1-1 on the season after tying the Cleveland Browns in Week 1.
Per ESPN.com's Jeremy Fowler, Brown appeared to get into a confrontation with offensive coordinator Randy Fichtner during Sunday's game.
Later, after quarterback Ben Roethlisberger ran for a one-yard touchdown in the fourth quarter, Brown went to the sideline by himself while the rest of the team celebrated.
Brown finished with nine receptions for 67 yards in the loss.
Following the game, former Steelers employee Ryan Scarpino took a shot at Brown on Twitter, which prompted Brown to respond Monday:
According to Fowler, Steelers linebacker Bud Dupree suggested Brown's trade comment was simply said out of frustration after a tough loss.
Tomlin told reporters Tuesday that Brown did not request a trade.
The 30-year-old Brown has been named to the Pro Bowl in each of the past five seasons, and he has been selected to the All-Pro first team in four consecutive campaigns.
He also has five straight 100-catch seasons and is coming off a 2017 season that saw him register 101 catches for 1,533 yards and nine touchdowns.
Brown and the Steelers are scheduled to travel to Tampa this week to face the Buccaneers on Monday Night Football.