She tweeted the bad news to fans: "This is my first time having to do this. I'm so, so sorry."
Within 20 minutes hundreds of followers had responded with get-well wishes, which were already among the most popular international trends on Twitter for the day.
Swift postponed the show until Oct. 11. She's due for a short break before returning to the road in Charlotte, N.C., on Friday in support of her multi-platinum "Speak Now" album.