The baby was killed in the capital Warsaw when a tree branch fell onto its stroller in a park, it said.
At least three other people, including a fire officer involved in a rescue operation, were killed by falling trees, while another died when gales blew him off his bicycle.
Two people were killed when a tree hit their car at Starogard Gdanski, while a tree also killed a car driver at Gizycko.
A farmer was killed under his own tractor when it capsized on a steep slope.
Road traffic was widely disrupted and tens of thousands were without electricity.