Graubunden canton officials said Wednesday the brown bear, identified by the tracking number M13, was awaken from its hibernation and came in contact with the girl and a couple of Italian tourists, The Local.se reported.
The girl was taken to a hospital and treated for shock after the bear followed her in town near the Italian border, officials said.
Switzerland's bear management plan provides for bears to be destroyed in if they're deemed to be a threat to humans.
M13 had caused problems in the Poschiavo area since last spring when it was anesthetized and tagged with a tracking transmitter after it attacked a goat, the Swiss news website said.
In September, the bear preyed on sheep and was injured by a train before it was caught.
A month later, officials erected an electric fence around a school in Poschiavo after the bear was found eating honey at an aviary outside the building.
In November, M13 broke into a shed where it spent 36 hours.
The Local.se said M13 was the first bear shot by Swiss officials since 2008.