The girl in Vernon Parish was the first reported fatality. The other deaths occurred in Calcasieu, Jackson and Acadia parishes.
Louisiana Gov. John Bel Edwards and Texas Gov. Greg Abbott said search and rescue teams continued to look for victims, but so far have found no reports of widespread fatalities.
Abbott credited the evacuations of thousands of people for preventing deaths in Texas while Edwards said they are only beginning to assess the damage.
Laura pounded the Gulf Coast with ferocious wind and torrential rain and unleashed a wall of seawater that was originally predicted to push 40 miles inland as the Category 4 storm roared ashore Thursday in Louisiana near the Texas border.
VIDEO: Hurricane Laura tears apart funeral home in Lake Charles
More than 600,000 homes and businesses were without power in the two states, according to the website PowerOutage.Us, which tracks utility reports.
The National Hurricane Center said Laura slammed the coast with winds of 150 mph at 1 a.m. CDT near Cameron, a 400-person community about 30 miles east of the Texas border. Forecasters had warned that the storm surge would be "unsurvivable" and the damage "catastrophic," though both governors said the storm surge appears to have been not as bad as they feared.
Abbott said the hurricane's storm surge hit the East Texas communities of Port Arthur, Beaumont and Orange "pretty hard" overnight, and the eye of the hurricane has continued to move about 100 miles north along the Texas-Louisiana state line.
PHOTOS: Hurricane Laura impacts Gulf Coast
The Associated Press contributed to this report.