The Vogue singer had been due to perform in Boston, Massachusetts on 2 December as part of the US leg of her global Madame X tour.
But in a statement on Instagram, she told fans she would be unable to perform on medical advice.
The 61-year-old said: “Please forgive this unexpected turn of events.
“Doing my show every night brings me so much joy and to cancel is a kind of punishment for me but the pain I’m in right now is overwhelming and I must rest and follow doctors’ orders so I can come back stronger and better and continue the Madame X journey with all of you.”
The three cancelled shows will not be rescheduled but refunds will be given to fans.
Live Nation, the tour’s promoter, said they could not move the shows to a different date at the Boch Centre Wang Theatre because of “tight scheduling”.
There is no announcement on the rest of the tour, which moves on to Philadelphia on 7 Dec, before a residence in Miami, Florida at the Jackie Gleason theatre, which will see out 2019.
Madonna returns to Europe in the new year, and will play 15 shows at the London Palladium in January and February.
She has had already had to rearrange dates on her latest tour, with a show in New York being rescheduled because of a knee injury.
Madonna had said the day before her cancellation announcement that she was taking her “usual Ice Bath for multiple injuries” after her show in Los Angeles.