Dark Souls 3, "the spectacular conclusion to From Software's trilogy", has had the biggest launch in the series, shipping 3m copies.
Comparisons are slightly confusing because of shipped units versus sold - they confused me (thank you commenters). In a similar timeframe, but in the US and Europe combined, Dark Souls 1 actually sold 1.2m copies, whereas Dark Souls 2 only shipped 1.2m copies. Even with only shipped figures for Dark Souls 3, it seems the game is comfortably ahead.
From Software's thematically similar PlayStation 4 exclusive Bloodborne sold 1m copies in under two weeks.