Most of the victims at the upscale Westroads Mall were shot inside the Von Maur department store near the children's clothing area.
"It was horrible, just horrible," one woman told local television station KETV, saying she hid under a rack of clothes when the gunfire started.
The Nebraska shooting was the latest in a series of mass killings that have shocked the US, where gun ownership is widespread and the right to bear arms is a fiercely contested constitutional issue.
The White House said it was a "terrible tragedy".
George Bush, the US president, was in Omaha on Wednesday on a fund-raising visit for his Republican party, but left the city about an hour before the shooting.
March 2005: A 16-year-old high school student kills five students, a teacher and a security guard at a school in Minnesota before killing himself.
October 2006: Five girls killed and five others injured after being taken hostage at an Amish school in Pennsylvania. Gunman Charles Carl Roberts kills himself.
February 2007: Gunman at Trolley Square mall in Salt Lake City kills five and wounds four before being shot dead by police.
April 2007: In the deadliest shooting in recent US history, student Cho Seung-Hui kills 32 people in rampage at Virginia Tech university before killing himself.
Thomas Warren, Omaha's police chief, identified the assailant as Robert Hawkins, 19, from Bellevue, Nebraska, near Omaha.
He was living with friends after going through a series of hard times, according to many who said they were close to Hawkins.
Warren said the dead were five females and three males but he would not specify whether any were children.
"It would be speculation to try to figure out what the motive may have been," said Warren. "It may be impossible to come up with an explanation."
Hawkins shot one man in the head from a third-floor balcony and others at point-blank range, witnesses said.
People said they hid in bathrooms and closets, some praying as dozens of shots echoed through the shopping centre.
Hawkins struggled with depression and had been in trouble at school and with the law, KETV reported.
He also recently lost a job at a McDonald's fast-food restaurant, it said.
Gun ownership is widespread in the US with an estimated 200 million guns in circulation among a population of about 300 million.
A survey in 2001 found about 39 per cent of all American households own at least one gun.
The issue of gun control and the constitutional right to bear arms is hotly debated.