Its developer said the web-slinger will be available as downloadable content (DLC) next year on one platform only.
The game will be released on 4 September across several platforms including PS4, Xbox One and PC.
Fans have suggested the move will see many players missing out on the game's full experience.
Sony has owned the movie rights to Spider-Man since 1999, and a video game headlined by the web-slinger - Marvel's Spider-Man - was a PlayStation 4 exclusive in 2018.
However, the superhero has appeared in other games on multiple consoles and PC over the years, including titles based on The Amazing Spider-Man film and its 2014 sequel.
Numerous fans shared their outrage on social media following the surprise announcement on Monday.
"As a PS and PC player, I'll just be skipping Avengers altogether now. This is a such a dumb thing to do," complained one gamer.
"I'm a PlayStation person and I still get a bit sad and mad when something like Spider-Man or stuff gets locked to only on PS. Xbox players really should be able to have fun too," said another.
Spider-Man will be made available to PlayStation players at no additional cost, and an in-game event will mark the release.
Ludo Medina, co-founder of gaming platform The N-Erd Council, told the BBC that the move would force many gamers to "pick sides".
"Exclusives are nothing new when it comes to games, but exclusive characters for specific consoles? This is a whole new territory.
"It is incredibly unfair on them and leaves PC and Xbox hanging out to dry. Gamers are saying it is forcing them to unnecessarily choose between one or the other."
Crystal Dynamics also confirmed the game's first post-launch character addition would be superhero Hawkeye, and would be available across all platforms.