Footage from local television station WVUE showed water spilling over a levee in Myrtle Grove, a community about 25 miles south of New Orleans.
There were also overtopped levees in Jefferson Lake and Point Celeste, WVUE reported, citing Louisiana Lt. Gov. Billy Nungesser. Flooding threatened to close Highway 23, a main artery out of lower Plaquemines Parish, Nungesser said.
There were no reports of high water rescues as of early Saturday afternoon.
VIDEO: Tree crushes car as Barry approaches Louisiana
Gov. John Bel Edwards said Saturday that none of the main levees on the Mississippi River in the state have failed or been breached so far because of Tropical Storm Barry.
But he warned at a news conference on Saturday that the storm is just beginning and the state faces significant threats in the days ahead.
Briefly considered a hurricane, Barry made landfall in Louisiana Saturday afternoon and weakened to a tropical storm. The storm's center was located about 5 miles northeast of Intracoastal City, and about 30 miles south-southwest of Lafayette, Louisiana.
Maximum sustained winds were clocked at 70 mph.
The Associated Press contributed to this report.