Martial, who has scored three times during pre-season, was in line to start through the middle against Graham Potter's side, but he picked up a hamstring problem against Atletico Madrid last weekend.
As a result, the France international will be absent on Sunday, and Ten Hag is unclear when the attacker will be available for selection once again.
"It is always difficult to say with these injuries, but hopefully not too long," the Dutchman told reporters after confirming that the 26-year-old would be missing against the Seagulls.
Cristiano Ronaldo will be in Ten Hag's thinking when it comes to a start despite the fact that the Portugal international has only played 45 minutes of football during pre-season.
"We need competition in the squad, but also we are going into a long season with a lot of games. We need a lot of good players. They are fit enough to start," the Man United boss added.
Luke Shaw has been spotted in training this week after missing out against Atletico and Rayo last weekend through illness, and the left-back is also expected to be fit.
Jadon Sancho was also unavailable for the two friendlies through illness, but it is unclear whether the England international will in the squad against Brighton.
Man United finished sixth in the Premier League table last season, 13 points behind fourth-placed Tottenham Hotspur, meaning that they will play in the Europa League in 2022-23.
Ten Hag will be tasked with leading the 20-time English champions back into the top four this term, and they will follow their opener with Brighton with a trip to Brentford on August 13.
Man United will then welcome bitter rivals Liverpool to Old Trafford on August 22 before ending the month with a trip to St Mary's to take on Southampton. body check tags ::