Worst hit was Moore, south of the city, where neighbourhoods were flattened and schools destroyed by winds of up to 200mph (320km/h).
About 120 people are being treated in hospitals. There are fears that the death toll will rise further.
President Barack Obama has declared a major disaster in Oklahoma.
He also ordered the federal authorities to join in the search and recovery efforts which are continuing throughout the night.
Monday’s twister hit Moore, a suburb of about 55,000 people, and remained on the ground for about 45 minutes.
The Oklahoma chief medical examiner’s office said 20 children were among the 51 confirmed dead.
Plaza Towers Elementary school took a direct hit: the storm tore off the building’s roof and knocked down walls.
“The school was flattened. The walls were pancaked in,” Oklahoma’s Lt Gov Todd Lamb told the BBC.
“There’s still roughly two dozen children that are missing. There have been some bodies recovered from that school and it’s absolutely horrific and devastating.”
Another school – Briarwood Elementary – was also damaged, and teachers were later seen leading pupils out to safety.
Oklahoma Gov Mary Fallin said it was a “tragic” day.
More than 200 Oklahoma National Guardsmen as well as out-of-state personnel have been called in to assist the search-and-rescue effort.
‘Most powerful tornado’
Shocked survivors spoke of the tornado’s power.
“We locked the cellar door once we saw it coming, it got louder and next thing you know is you see the latch coming undone,” survivor Ricky Stover said.
“We couldn’t reach for it and it ripped open the door and just glass and debris started slamming on us and we thought we were dead, to be honest.”
Melissa Newton said: “There’s shingles and pieces of sheet rock and wood in our yard and all across our neighbourhood. Some homes are completely gone. It’s devastating.”
James Rushing said he had rushed to Plaza Towers Elementary School, where his foster son Aiden was a pupil, to see it destroyed by the storm.
“About two minutes after I got there, the school started coming apart,” he told the Associated Press news agency.
The National Weather Service (NWS) said Monday’s tornado had generated winds of up to 200mph.
“It’s certainly the most powerful tornado that I’ve ever dealt with in my 20 years with the weather service,” NWS meteorologist Rick Smith in Norman, Oklahoma, told the BBC.
The town of Moore was hit by a severe tornado in May 1999, which had the highest winds ever recorded on Earth.
But Betsy Randolph of the Oklahoma Highway Patrol told local news station Skynews 9 that the damage on Monday appeared to exceed that of the 1999 tornado.
Tornadoes, hail and high winds also hit Iowa and Kansas, part of a storm system stretching from Texas to Minnesota.
On Sunday, a tornado smashed a trailer park on Highway 102 near Shawnee, Oklahoma.
Oklahoma’s state medical examiner confirmed earlier on Monday that two people had been killed in the area.