The Piper PA-32 single-engine plane went down Tuesday evening in a neighborhood of modest, single-family homes near Hawkins Field Airport.
Hinds County Coroner Sharon Grisham-Stewart confirmed three people died. She said dental records or DNA would be needed to confirm their identities.
A hospital spokesman says one patient from the scene was in good condition at University of Mississippi Medical Center. He would not give details citing privacy laws.
A Jackson deputy fire chief told WJTV-TV that one person escaped the burning home with minor injuries but it was not immediately clear if anyone else was inside.
The Piper PA-32 single-engine plane is registered to a company in Flowood, Miss., said Federal Aviation Administration spokeswoman Kathleen Bergen. She did not immediately have information about the condition of the people aboard the plane.
Witnesses say large flames and black smoke rose about 50 feet from a burning house that was hit in the neighborhood of modest, single-family homes surrounded by big magnolia and oak trees about a half-mile from the zoo.
The FAA says the plane had just departed Hawkins Field Airport headed for Raymond, Miss., when it crashed.
Vivian Payne, who lives about six blocks from the crash site, said that about 5 p.m., she heard a loud bang that sounded different from an electrical transformer blowing.
"It shook the walls of my house," Payne said as she stood among ambulances, police cars and fire trucks, their lights flashing in the chilly night air.
The weather in Jackson is partly cloudy in the 40s.