Some players have reported that update files have been as large as 84GB, which would take several hours to download on an average UK home broadband connection.
Activision said that the problem was affecting some Xbox One players.
The update adds new weapons, maps, bug fixes and narrative elements to the popular first-person shooter.
Call of Duty: Modern Warfare already takes up a large amount of space on console hard drives – on PS4, the installed game can amount to almost 200GB in total.
The phrase “84GB” began trending on Twitter as news of the outsized update spread.
Many players expressed their dissatisfaction with the size of the file.
One commenter wrote: “Warzone is literally going to be the only game on my Xbox and that’s getting closer to being the case every update. I want my storage back. Refunded.”
The latest update was originally scheduled for release on 3 June, but Infinity Ward, the game’s developer, held it back to avoid drawing attention from the ongoing anti-racism protests prompted by the killing of George Floyd while in the custody of Minneapolis police.
Infinity Ward said the update was postponed to allow people to focus on “equality, justice and change”.
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