Storms and tornadoes have lashed the region in recent days, swelling rivers and causing flash flooding.
Missouri Governor Jay Nixon said 13 people in the state had died.
Another seven have died in Illinois, where there is a disaster proclamation in seven counties.
Mr Nixon said the National Guard had been called in to help local authorities.
Aerial footage showed water from the Mississippi River engulfing buildings in the evacuated town of West Alton, north of St Louis, on Tuesday.
In the town of Union, about 50 miles (80km) west of St Louis, buildings were partly submerged by severe flooding from the Missouri, Meramec and Bourbeuse rivers.
Coast Guard spokesman Capt Martin Malloy said the high water levels and fast currents had led them to close the section of the Mississippi near St Louis - a busy route for commercial shipping.
River levels are forecast to peak on Thursday and Mr Nixon warned that the situation could get worse before it gets better.
He said the National Guard would provide security in evacuated areas and direct traffic away from closed roads.
"These citizen soldiers will provide much-needed support to state and local first responders, many of whom have spent the last several days working around the clock responding to record rainfall and flooding," he said in a statement.
Nr Nixon added that three new flood-related deaths had been discovered on Tuesday, raising the death toll in the state since the storms began over the weekend to 13.
Many of the victims have been trapped in vehicles swept off flooded roads.
South-west of St Louis, a section of Interstate 44 was closed by flooding near the town of Rolla while part of Interstate 70 was also closed in the neighbouring state of Illinois.
Many other smaller roads were also closed across the two states, where flood warnings were in effect.
Floods also inundated a wastewater treatment plant south of St Louis on Monday, causing sewage to flow directly into rivers and streams.
The flooding in Missouri and southern Illinois began over the weekend after as much as 10ins (25cm) of rain fell in some areas in a matter of hours.
It came after severe storms over the Christmas holiday claimed at least 49 lives across southern and western states of the US.
Parts of eastern Oklahoma, Arkansas and Illinois are still subject to flood warnings.
A five-mile (8km) section of the Mississippi River near St Louis, Missouri, has been closed to vessels as rising water levels caused "hazardous conditions", the US Coast Guard said.