The hit crime game is one of the most popular video games of all time, with sales still strong despite being released in 2013.
Free games are available every week on the Epic Games Store; the previous release was an indie game called Death Coming.
The offer is only valid for the Windows PC edition of the game.
In order to download Grand Theft Auto V before the week is up, users must enable two-factor authentication on their Epic Games accounts.
Epic has offered free games on its platform since 2019, and will continue to do so weekly for the duration of 2020.
While players will no longer be able to download the game after 21 May, those who have downloaded it are able to keep and play the game forever.
When the Grand Theft Auto giveaway first began, at 4pm on 14 May, the Epic Games website crashed due to a massive influx of visitors.
Grand Theft Auto V follows the interlinking lives of three violent criminals in the fictional state of San Andreas.
As well as a substantial single-player campaign, the game also boasts a thriving multiplayer community.
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