Electricity network operator AusNet reported 72 separate outages across the south of the country, where wind gusts hit 113 kilometres (70 miles) per hour.
Some 19,300 customers were said to be affected.
The Victoria State Emergency Service has issued a "severe weather" warning for Wednesday and into Thursday, telling people to stay away from trees and fallen power lines.
The Bureau of Meteorology reported wind gusts of more than 100 kilometres (62 miles) an hour in several locations east of Melbourne. Winds were expected to ease gradually overnight.
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