The Sing hitmaker has sold out three summer gigs at the fabled venue, which holds a capacity of 80,000 people, and grumpy Gallagher is far from happy.
He tells Britain's NME magazine, "I don't think I can live in a world where that's even possible."
He continues, "When you hear that kind of polished pop and then there's a ginger guy with a f**king guitar, it seems subversive, but it's f**king not."
Gallagher, who has performed at Wembley with Oasis, goes on to discuss the current state of pop music, and his dismay with the direction it's going.
He adds, "It’s a strange time, and it seems like the whole thing is embedded for good now, for f**king forever. It's not all over, but it'll go back to the way it was in the early '80s where indie bands are the alternative thing, the lower level.
"In the early '80s everyone at indie labels, even major labels, were trying to push this music to the fore because everything else was s**t, and maybe it'll happen again, but I don't see it for the next decade."
But Sheeran, who has become one of Britain's biggest acts thanks to the success of his chart-topping album X, fired back at Gallagher's comments on Twitter.com, simply writing, "I can live in it, it's really enjoyable."