"Barry expected to be a hurricane by landfall on Saturday," the NHC said in an alert on Friday.
The NHC also said heavy rains and dangerous storm surges are expected across the north-central Gulf Coast.
Maximum sustained winds had reached 65 miles per hour as of early Friday evening, according to the alert.
Southwest Airlines cancelled all flights from the New Orleans, Louisiana airport, the company said in a statement on Friday.
New Orleans Mayor LaToya Cantrell in a tweet told residents to "shelter in place" by 8:00 p.m. EST (midnight on Saturday GMT).