Among the victims was a 14-year-old girl who was killed when a tree fell on her house, Xinhua news agency quoted Louisiana Governor John Bel Edwards as saying on Thursday.
He warned that the number of casualties would grow as thousands of local, state and federal officials were conducting search and rescue operations, surveying damage and restoring water and power.
Spared the worst case of flooding and storm surge, Louisiana has caused "tremendous damage" from winds caused by the storm.
Besides, more than 600,000 homes and businesses were without power and it was not clear how long power would be out.
Louisiana Department of Health also said at least 67 water systems are "inoperable", meaning more than 200,000 people are potentially having trouble accessing clean water.
In Texas, Governor Greg Abbott on Thursday flew above the affected region with the US Coast Guard to conduct a full survey of the damage.
Abbott said Orange city in East Texas was hit hard by the storm.
"You saw more rooftops ripped off," he said, adding: "You saw big pieces of steel framing wrapped around some trees. You saw some roads that were still inundated under water."
Laura made landfall in Louisiana's Cameron Parish as a Category 4 hurricane around 1 a.m. Thursday, making it the most powerful hurricane to hit Louisiana in 150 years.
It brought winds of a maximum speed of 240 km per hour and heavy rainfall.
Laura has weakened to a tropical storm, bringing heavy rains and tropical storm force winds over parts of the state of Arkansas, the National Hurricane Center said.