Generally no, although some women do have lymph nodes within the breast, and they can experience some tenderness in these intra-mammary lymph nodes during viral illnesses (also, flu viruses and other viral infections can cause generalized muscle and body aches, including in the area of the breasts). Breast pain is also very common around the time of a woman's menstrual periods, and if a period happens to coincide with an acute viral illnesse, then it might appear that a viral infection is causing the breast pain.
Of course, it is important to see your doctor if you are experiencing new breast masses, nipple discharge (especially a bloody discharge), nipple retraction or skin dimpling, or other new and persistent breast problems.
Sincerely/ Robert A. Wascher, MD, FACS
http://doctorwascher.com