The chart-topping position follows news that the game was the biggest entertainment launch of all time.
Next was fellow new entry Elder Scrolls V: Skyrim, which debuts in second.
Elsewhere, last week's number one Battlefield 3 drops to third, Uncharted 3 sinks to sixth while Moshi Monsters debuts in seventh.
The top ten in full:
1. (-) Call of Duty: Modern Warfare 3 (Activision)
2. (-) Elder Scrolls V: Skyrim (Bethesda Softworks)
3. (1) Battlefield 3 (Electronic Arts)
4. (3) FIFA 12 (Electronic Arts)
5. (5) Just Dance 3 (Ubisoft)
6. (2) Uncharted 3: Drake's Deception (Sony)
7. (-) Moshi Monsters: Moshling Zoo (Mind Candy)
8. (4) Batman: Arkham City (Warner Bros. Interactive)
9. (8) Zumba Fitness (505 Games)
10. (-) Wii Party (Nintendo)
Leisure software charts compiled by Chart Track, (C) 2011 UKIE Ltd.
Watch the Modern Warfare 3 live-action trailer below: