Among other stuff: the final of the UEFA Championship -as mentioned earlier- (btw, a good opportunity to see FC Barcelona taking the title 'again'), an Ed Sheeran concert is supposed to be happening in Madrid also around those dates, the 78th Book Fair at Paseo Recoletos (pending tba)... Sometimes, like in other big cities, several large events coincide in time and hotel availability decreases as fast as prices increase.
In any case, the Wanda stadium isn't that large, barely 68.000, so it's unlikely this event on its own is causing this "shortage", moreover noting that a number of the fans attending the match will be members of the club, therefore they live in or near Madrid (and don't need any accommodation).
... or maybe is that @pjsdoc will be in town, and everybody wanna have a glimpse, lol!
As Ann mentioned, have a look at 'hostals' (not hostels!), which are sort of basic hotels and thus are cheaper, after all, you're going to use it only to crash at night, right? Btw, the Spanish word is "hostal", and "hostales" in plural.
Another option would be an apartment, even if it's only for a couple of nights. For that Airbnb, Homeaway, Bookings.com...
Good luck!