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.

Bristol Crown Court heard that Vielstone and Gatooma homes in Devon had a room where residents were left alone, often without food and water.
Paul Hewitt, 70, denies charges of conspiracy to detain and falsely imprison residents.
Mr Hewitt also said he was unaware that residents missed meals and he would have "made sure" they were fed.
The court heard that a woman resident said she had been tied up in the room at Gatooma in Holsworthy
Mr Hewitt, from Teignmouth, said he would not approve of this, telling the court: "Absolutely not. Mechanical restraint was a no no."
He also denied stopping residents making home visits as a punishment.
Mr Hewitt said he purchased Gatooma in 2004 for residents with behavioural issues.
"It was about giving them a better quality of life," he said.
"They had been in hospital or locked units. We wanted them to be free to be part of a community set up and be free to go to the shops or the pub."
Mr Hewitt, founder of Atlas Project Team Ltd, ran the two care homes for adults with learning disabilities.
He sold the business in 2006 but continued to be in charge, the court heard.
Mr Hewitt and employees Lee Farrant, 30, James Lawson, 41, Julie Barlow, 51, and Aaron Jones, 33, all from Devon, deny a series of charges against seven residents at Vielstone near Bideford and Gatooma in Holsworthy between 2010 and 2011.
Mr Lawson denies eight charges of false imprisonment, Mr Farrant six charges of false imprisonment and Mr Jones and Ms Barlow three charges each of false imprisonment.
The trial continues.

The 30-inch sword was found by Goran Olsen, a hiker who found it when he sat down to rest.
Experts say it's in surprisingly good condition after surviving hundreds of years of frost and snow.
The ancient weapon will be able to help archaeologist work out how people lived in Viking times.
The sword will go on display at the University Museum of Bergen.
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.
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The boss of two care homes said he was unaware vulnerable residents were being locked in so-called punishment rooms.
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A twelve hundred year old Viking sword has been found buried in rocks in southern Norway.