Saliba was forced off at half-time during Sunday's 1-0 Premier League win over Crystal Palace, while Martinelli limped down the tunnel after coming on as a substitute late in the game.
Arteta confirmed that both players will miss the tie and require further assessment to determine the severity of their injuries.
"He's out. We are assessing him but he won't be involved in this match," Arteta said of Saliba, before adding on Martinelli: "It looks as well he's going to be out. We have to do some more tests and see the extent of the injury, but this game is going to be too early for him."
The absences further deplete Arsenal's attacking options, with Noni Madueke, Kai Havertz and Gabriel Jesus already sidelined.
Pre-season signing Viktor Gyokeres, who began his professional career at Brighton, has led the line in all 12 of Arsenal's league and Champions League matches so far, scoring five goals, but Arteta is expected to manage his workload carefully.
"In the front line, that's where we have more difficulties," he admitted. "We have to be careful because we don't have that many options. We're going to try to manage the load as best as possible to keep the team fresh and competitive."
There was some positive news for Arsenal as Arteta confirmed Declan Rice, Riccardo Calafiori and Bukayo Saka are all available to face Brighton after minor knocks.
The Gunners head into the tie four points clear at the top of the Premier League with seven wins from nine matches, and Arteta welcomed the growing optimism around the club.
"That's what we want," he said. "When people are excited and see the team competing consistently, those are the right reasons to believe. We're in a good position, but we know how early it is and how difficult every game will be."