The player's absence was confirmed by Arsene Wenger at his press conference on Wednesday; the manager also confirmed he would miss the trip to Stoke City in Week 2.
"He had a little abdominal strain that he caught in training on Sunday morning before he came to Wembley," said the coach, per Sky Sports News. "He had a scan two days ago and he's out for a while. I don't know [how long he will be out]—two weeks, one more week. He will not be available. He will not play at Stoke."
Alexandre Lacazette's arrival in the summer gave the Gunners invaluable strength in depth going forward, while the likes of Alex Iwobi, Alex Oxlade-Chamberlain and Theo Walcott can provide cover for Sanchez on the flanks.
None of the trio can compare to him in terms of output or the attacking threat he carries, though, so his loss is a real blow.
He was by far the Gunners' most potent weapon last year, with 30 goals and 19 assists to his name in all competitions, per Transfermarkt.
The Chilean also seems to possess a far greater hunger for victory than many, if not all, of his team-mates—a quality that sets him apart and helps drive him forward in difficult situations.
Arsenal aren't entirely reliant on him for goals, but perhaps none of their players are on quite Sanchez's level, making his fitness paramount if the Gunners are to fulfil their ambitions.
As noted by Sky Sports News, Sanchez has been strongly linked with a summer departure from Arsenal, with Manchester City and Paris Saint-Germain interested in signing him.