The Omaha World-Herald said Douglas County Attorney Don Kleine confirmed the industrial accident at International Nutrition killed at least two people, whose names were not released.
Interim Fire Chief Bernard Kanger told a news conference there were fatalities but declined to say how many until a search of the building is completed.
Kanger said 10 people have been transported to area hospitals. The chief said four were in critical condition and six had non-life-threatening injuries, the World-Herald reported. Seven more of the injured declined medical attention.
A search team was expected to enter the plant later Monday.
The newspaper said there were 38 people working at the plant.
WOWT-TV, Omaha, said workers reported hearing a "loud snap" and heavy smoke as the building collapsed from its third floor down. Those who escaped said the building was entirely dark and many had to feel their way toward exits or use cellphones for light, the World-Herald reported.
Officials contacted Nebraska's Urban Search and Rescue Team in Lincoln for assistance, the television station said.
On its Twitter page, the Omaha Police Department posted notification of the collapse and pictures. One of the posts read: "Smoke getting heavier. Please stay back. Large #OFD presence in the area. #OPD restricting access."
One firefighter was injured, but Kanger said the firefighter's injuries were not considered life threatening.
Kari Cook told WOWT her fiance, John Broderick, a supervisor who was on the building's second floor, texted her: "Major accident. I'm hurt and trapped. I love you."
At first she thought it was a joke but as word quickly spread, Cook and other family members of workers at the facility rushed there. The World-Herald said family members were assembled in an adjacent parking lot with a fire department chaplain, awaiting word on their loved ones.
The makeup of the facility itself isn't entirely clear. WOWT said the building does not contain any toxic chemicals. Fire officials said they are still unsure what triggered the collapse and are investigating initial reports of an explosion before the building went down.
Celebrity Families of 2014 [PHOTOS]