The storm is set to be fully ashore by Saturday, with concerns that rainfall could trigger flooding in and around New Orleans.
Mr Trump declared the emergency on Friday, authorising the Department of Homeland Security and the Federal Emergency Management Agency to coordinate relief efforts should it need to.
National Guard troops and rescue crews have been stationed around the state with boats and high-water vehicles.
Meanwhile, helicopters were on standby as drinking water and blankets were made ready for distribution.
Utility repair crews with bucket trucks moved into position in the region as some homeowners sandbagged their properties or packed up and left.
Forecasters said Barry could unload 25 to 50 centimetres of rain across a swath of Louisiana including New Orleans and Baton Rouge, as well as southwestern Mississippi.
Some areas of Louisiana could even see 63 centimetres, while some low-lying roads near the coast were already covered with water Friday morning, as the tide rose and the storm pushed water in from the Gulf of Mexico.
The National Hurricane Centre predicted Barry would come ashore as the first hurricane of the Atlantic season, just barely over the 74 mph windspeed threshold.
Though the centre's director Ken Graham said the designation is "not the point here" and the real danger, he said, is the rain.
Barry's downpours are expected to pose a severe test of the improvements made to New Orleans' flood defences, since the city was devastated by Hurricane Katrina in 2005.
New Orleans could get its worst downpour in decades, possibly eclipsing the city's wettest day on record of 32 centimetres on May 8, 1995, forecasters said.
The storm could also shatter Baton Rouge's one-day record rainfall of 30 centimetres from April 14, 1967.