https://www.gamespot.com/articles/fortnite-season-6-release-date-confirmed-for-next-/1100-6461854/

After 10 weeks of challenges, Fortnite Season 5 is drawing to a close, which means Season 6 of the phenomenally popular (and matrimonially detrimental) battle royale game is just around the corner. Developer Epic Games hasn't formally announced when the new season will begin, but all signs indicate that Season 6 will kick off next week. We still don't know what to expect, but the mysterious cube plunged into Loot Lake after making its way around the map. [Update: Season 6 officially begins on September 27, giving a day of breathing room between the end of the current season and the start of the new one.]

According to the official Fortnite website, Season 5 is set to conclude on Tuesday, September 25. In the past, Epic would begin a new season just as the previous one was ending, which suggests that Season 6 should arrive shortly after Season 5 officially wraps up. Tuesday is also typically the day the developer rolls out a new Fortnite update, further suggesting that Season 6 will start early next week.