Firefighters said the tarp was not on the tower when the high winds hit, but was being stored alongside it.
The tarp landed on some trees as well and also damaged a fence along Stevens Drive, according to the fire department.
Utility crews later removed the tarp and said no power outages were reported in the area.
No one was hurt.
Crews said that the tarp was originally being used to ensure that debris from sandblasting and paint did not fall onto nearby homes during maintenance work.