Demolition of the Phoenix parking garage, which the city deemed too dangerous for use and with problems too costly to repair, began Tuesday.
A 28-foot concrete panel weighing 7 tons fell from the upper deck of the city-owned garage in May.
Hernando Alley and Water Street will be closed during demolition, and cars leaving the Annex Garage must exit onto Main Street until Friday.
While Water Street is closed, people parking in the Lexington Public Library's garage also will need to exit via Main Street.
That means traffic will be two-way instead of one-way, so parking in the library garage's breezeway will be prohibited during this time.
There will be some lane and sidewalk closures on Vine Street during off-peak hours, the city has said.
Demolition should be finished by the end of February. The resulting vacant lot will be used for surface parking.