The attack happened Wednesday in Muncy Creek Township, which is located about 16 miles east of Williamsport.
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The Pennsylvania Game Commission says the woman was outside with her dog when the bear attacked.
Game Warden Supervisor Mike Steingraber says the woman was able to free herself and call for help.
WNEP-TV reports that the woman has been hospitalized in critical condition. Her dog was also injured.
It is unclear why the bear attacked.
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Steingraber says it may have been attracted to deer parts from a recent hunting trip that were left near the home.
Game wardens are now searching for the bear, and multiple bear traps have been set up.
The bear will be euthanized.