Nearly 100 patients at the St John Regional Medical Center in Joplin were having to be evacuated from after the hospital took a direct hit.
A resident living 45 miles (70km) away said debris from the hospital had landed in his yard, including medical supplies and X-rays.
At a pre-dawn news conference on Monday outside the St John Regional Medical Center, Mr Rohr announced that the number of confirmed dead was 89.
He said the tornado had cut a path nearly six miles long and more than half a mile (800m) wide through the city centre, and that tornado sirens had given residents about a 20-minute warning.
Fire chief Mitch Randles said the tornado “cut the city in half” and estimated that 25 to 30% was damaged.
A door-to-door search of the damaged area will begin later on Monday morning, but progress will be slow because of the danger of downed power lines and gas leaks, which caused fires around the city overnight.
“We will recover and come back stronger than we are today,” Mr Rohr said.
Earlier, the Red Cross opened a shelter at Missouri Southern State University in Joplin for victims, spokeswoman Joanne Muir told the BBC.
It had also sent an emergency response vehicle with some supplies such as blankets, cots, water and food to the area, she said.