The song, which riffs on The Sound of Music's My Favourite Things, was played 16.9m times last week, a chart record.
Mariah Carey's All I Want for Christmas is You was the previous record-holder, with 15.3m plays in a week last month.
7 Rings is also the first single to sell more than 100,000 copies since the Grenfell charity single in June 2017.
Grande's song is a tongue-in-cheek hymn to retail therapy, inspired by a trip to Tiffany's last year, where she bought her friends matching diamond rings.
