The town suffered a "direct hit" from the tornado and parts of the city have been devastated, local media says.
Missouri Governor Jay Nixon has declared a state of emergency and warned more storms are on the way.
Last month, tornadoes and storms killed at least 350 people in Alabama and six other southern states.
John Miller, a freelance photographer for the Springfield News-Leader newspaper, described widespread damage in Joplin.
"The Home Depot is levelled. The Walmart is destroyed. Gas stations, buildings. Everywhere I could see was either heavily damaged or completely destroyed," he said."I saw firefighters and paramedics pull a young girl out of a car at the Home Depot. Part of the building had fallen on the car."
Hospital damaged
Power lines and phone lines in the city are down, reports say.
Witnesses said ambulances lined the street near a Walmart store amid reports that hundreds of people were trapped inside.
Officials at St John's Hospital in Joplin said the building had been badly damaged and windows blown out. A resident living 45 miles (70km) away said debris from the hospital had landed in his yard, including medical supplies and X-rays.
Rescuers search for trapped residents in Joplin In many cases rescuers are using their bare hands to reach survivors
Newton County Coroner Mark Bridges told Reuters by telephone that at least 30 people had been killed.
The Red Cross has opened a shelter at Missouri Southern State University in Joplin for victims of the disaster, Red Cross spokeswoman Joanne Muir told the BBC.
It has also sent an emergency response vehicle with some supplies such as blankets, cots, water and food to the area.
"I know the hospital did take a direct hit and I have heard from people that some people have lost their homes, and there was damage to one of the schools," she said.
