Boston announced Brown will not play in Game 1 of the second-round series due to a right hamstring strain.
A Celtics team that has been without Gordon Hayward since the season opener and lost offensive leader Kyrie Irving in mid-March will be put even further to the test with Brown sidelined.
The Celtics noted Marcus Smart will take Brown's spot in the starting lineup.
The California product suffered the injury during Game 7 of Boston's first-round series against the Milwaukee Bucks on Saturday and wasn't able to return on a short turnaround heading into the battle with Philadelphia.
Brown was a vital part of Boston's offense against Milwaukee, scoring 20 points in Game 1, 30 points in Game 2 and 34 points in Game 4. He provides important outside shooting to help space the floor for fellow swingman Jayson Tatum and big man Al Horford, but he can also attack the rim off the bounce if the opportunity presents itself.
The No. 3 overall pick of the 2016 draft averaged 14.5 points and 4.9 rebounds per game while shooting 39.5 percent from three-point range during the 2017-18 regular season.