So far, no one has been reported killed, which authorities hope will remain true.
But at least two people were critically injured in Lamar County, the Mississippi Emergency Management Agency said.
The tornado struck Hattiesburg, the southern Mississippi city that straddles Lamar and Forrest counties.
Hattiesburg mayor Johnny DuPree reported major damage to structures around town. "If there is a good thing about this, it happened on a Sunday when most of these structures were vacant," he said.
The state emergency management agency said seven counties have reported damage. Several homes were destroyed in Marion County, and numerous homes, businesses and public buildings sustained "significant damage."
As of Monday morning, about 4,000 power customers are without electricity, Mississippi Power said. That's an improvement from the 13- to 14,000 customers who were without electricity at one point, but it's unclear when power would be restored to everyone, spokesman Mark Davis said.
Mississippi Gov. Phil Bryant declared a state of emergency for counties affected. The declaration allows for the use of state resources and assets to support local response efforts, MEMA said.
iReporter shopping at Target captures video of tornado
Hattiesburg is home to the University of Southern Mississippi. It suffered damage to several buildings, but there were no reports of injuries there.
University police declared a state of emergency and urged those not on campus to stay away until further notice.
Nearby Oak Grove High School also suffered damage. Randy Wright posted photographs to his Twitter account of the school, showing debris strewn on what looked to be a parking lot and a truck upside down in a baseball diamond.
The Hattiesburg Public School District canceled classes Monday. The university campus will also be closed.
"There's quite a few homes without power at this point. Quite a few trees on houses, on cars, that type of thing," said Forrest County Sheriff Billy McGee.
He said between 10 to 15 people were hospitalized, but that none suffered serious injuries.
It was not clear how those people were hurt.
Sarah Lawrence, a Hattiesburg resident, said that the storm sounded like "stuff being thrown."
"Within seconds, everything changed," she said. "I didn't feel like there was much notice. I heard the sirens and everything looked OK outside, so I started making preparations to go into the bathroom. And then, next thing I know, all the lights went out, and it got dark outside."
HATTIESBURG, MS (CNN) -- A tornado touched down in southern Mississippi on Sunday, injuring at least three people and causing significant damage, state officials said.
As the storm system moved east, tornado warnings remained in effect for parts of southeastern Mississippi and southwestern Alabama.
"Right now, the most important thing for us is to make sure that we account for all individuals and make sure that they're safe and secure," Robert Latham, director of the Mississippi Emergency Management Agency, told CNN.
He said there were reports of significant damage in Hattiesburg, where the tornado touched down. The city is home to the University of Southern Mississippi.
"I hope to goodness that when all this is said and done, all we have to do is clean up a mess and that we haven't lost any lives in this," Latham said.
Sara Lawrence, a resident of Hattiesburg, said that the storm sounded like "stuff being thrown."
"Within seconds, everything changed," she told CNN. "I didn't feel like there was much notice. I heard the sirens and everything looked OK outside, so I started making preparations to go into the bathroom. And then, next thing I know, all the lights went out, and it got dark outside."
Brett Carr, with the Mississippi Emergency Management Agency, reported that the three injured people were in Marion County. It was not immediately clear how they were hurt.