Yes there are, although they are necessarily limited to general surgery trained residents. Some are open to OB-GYNs as well.
The match is administered by the Society of Surgical Oncology (http://www.surgonc.org/default.aspx?id=60) and has been around for 4 years, although breast fellowships have been around for nearly 25 years in some form or another.
These are NOT plastic surgery fellowships, so although some time rotating on plastics is required by the SSO, if one desires to learn aesthetic breast reconstruction, these are not the right fellowships. These fellowships are designed for those who have an interest in breast oncology and diseases. The year or two of training encompasses radiation oncology, medical oncology, pathology of breast lesions, mammography, genetic counseling, psychosocial concerns of breast cancer, post-mastectomy breast reconstruction and of course, breast surgery for benign and malignant lesions. You are trained in biopsy techniques to a varying degree depending on the program.