Getting a massage after fat transfer to breasts

Thanks so much for your question,

Most surgeons recommend waiting 6 to 8 weeks before applying any significant pressure to the breasts—including lying on your stomach or having a massage that puts weight on your chest.

Week 8-10: You may be cleared to lie on your stomach or have massages—only if your healing is on track and your surgeon agrees.

Sincerely,
Dr. Emmanuel Mallol

You will receive varying opinions in answer to your question. It would be most appropriate to discuss this with your surgeon. He or she would appreciate your following their personal instructions as they are ultimately responsible for your outcome.

Dear Fierce2456,
I understand your concern. It is best that you consult your plastic surgeon regarding post operative care and management (i.e including massage techniques and timing) specific to your case. Your surgeon knows your condition well and has preferences on when and what to use for faster healing and recovery. Post operative care and management depends on the type of surgery performed and the technique used during surgery among other factors.It is best, however, that you follow your plastic surgeon's advice on post operative care management for a smooth and faster healing and recovery.
Daniel Barrett, MDCertified, American Board of Plastic SurgeryMember, American Society of Plastic SurgeryMember, American Society of Aesthetic Plastic Surgery

That is advice that you would need to get from your surgeon. There is no evidence that lying on your stomach may affect the result but each surgeon will have a different idea regarding this

No, I suggest waiting at least 3 months to allow the fat grafts to survive and settle. After about 3 months, the grafts are stable enough for some pressure. For now, do the massage on your sides or back, or possibly the chair.