Glenda,
Yes, women can have a mastitis without lactating.  This is from Susan Love's
book:

Nonlactating mastitis may occur in women who've had lumpectomies followed by
radiation, in diabetics, or in women whose immune system is otherwise
depressed: such women are prone to infections, either because some of the
lymph nodes, which help fight infection, have been removed, or because their
immune systems are generally less strong than those of most people.  This
type of infection will usually be cellulitis -- an infection of the skin --
red, hot, and swollen all over rather than just on one spot.  It's generally
accompanied by high fever and headache: both characteristics of a strep
infection (staph infections, by contrast, are usually local).  It will be
treated by your doctor with antibiotics, usually penicillin, and you may be
briefly hospitalized.
Skin boils (or staph infections can form on the breast, as they can on other
parts of the body.  If you're a carrier of staph and prone to infection as
well -- as in the case of diabetics -- this is more likely to occur than in
noncarriers or people less infection-prone.  It's also possible to get an
abscess in the breast when you're not lactating and don't have any of the
other risk factors, although this is unusual.

Hope this was helpful.  This is from her 1990 edition.
Ann Perry RN IBCLC
Boston, Mass

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