Several people in the crowd were injured in the crash in front of the iconic Tiananmen Gate around noon, a statement posted on the Beijing police's microblog said.
It said the vehicle burst into flames after crashing into one of the ancient stone bridges leading to the gate. No other details were given, and it wasn't clear whether the incident was accidental or deliberate.
Traffic along Changan Avenue that runs in front of the gate appeared to be largely uninterrupted, although Beijing's subway announced it was closing the station closest to the gate and one of the exits in the adjacent station.
Tiananmen Gate is one of the southern entrances to the former imperial palace and stands across from several lanes of busy traffic from the sprawling Tiananmen Square. It is usually thronged by tourists from China and overseas, raising the possibility that large numbers of people could have been hurt.
The area around the square is one of China's most closely guarded and politically sensitive public venues. Just to the west lies the Great Hall of the People, the seat of China's parliament, while many of China's top leaders live and work just a few hundred meters (yards) away in the tightly guarded Zhongnanhai compound.
Tiananmen Square is also heavily policed to guard against political protests as occasionally happens on sensitive dates.
The square was the focus of a 1989 pro-democracy movement that was violently suppressed by the military.
Pictures posted on Chinese social media sites showed the blazing shell of the SUV and a plume of black smoke rising close to the portrait of communist China's founder hanging on the towering wall of the former imperial palace.
There were also police vehicles gathered, and crowds looking on.
Several of the pictures were deleted within minutes, streets leading to the square were blocked off, screens were erected and two AFP reporters were forcibly detained close to the site, with images deleted from their digital equipment.
"A jeep crashed into the guardrail on Jinshui Bridge, then caught fire," the Beijing police said in a statement on their verified social media account. The Jinshui Bridge passes over the moat around the Forbidden City.
"It is confirmed that the jeep driver and the two other people in the car are dead," the statement said.
"On its way, it injured many tourists and police officers. Police are currently doing their job by rescuing people on the spot, and the fire has been extinguished," it added.
Victims were sent to nearby hospitals for treatment, it said.
Beijing transport authorities said via social media that a subway station next to the square had been closed at the request of police.
One 58-year-old Italian tourist said he had been visiting the Forbidden City when officers came in around noon and told everyone to leave.
Tiananmen Square is the symbolic centre of the Chinese state and is generally kept under tight security, with both uniformed and plain-clothes personnel deployed, many of them equipped with fire extinguishers.
Details on a motive were not immediately available, but Chinese social media users speculated that it could have been intentional.
"Is this the 2013 Tiananmen self-immolation incident?" asked one poster. "There's still a person inside the car!"
Another poster asked: "Could it be a terrorist attack?"
Around 120 Tibetans have set themselves alight since February 2009 in Tibet itself and adjoining regions of China, in protest against what they see as Chinese oppression.
News of the incident first trickled online Monday afternoon in reports from Chinese social media users on the scene.
Pictures they posted showed the flaming wreck surrounded by several police and emergency vehicles, directly in front of the sign on the Tiananmen gate reading: "May the great unity of the world's people last for 10,000 years."
Soon afterwards police erected high curtain-like barricades directly in front of the Mao portrait, blocking passers-by from viewing the scene.
The square is flanked by several of communist China's key buildings and institutions, with Mao's mausoleum on the south side, the Great Hall of the People to the west, and China's national museum to the east.
The imperial Forbidden City, a world heritage site that sees 14 million visitors a year, is on the north side, with the Tiananmen Gate as its entrance, where Mao proclaimed the foundation of the People's Republic of China in 1949.
A huge flagpole stands at the northern end of the plaza, with a giant national flag fluttering from its top.
Chang'an Avenue, the main road passing from east to west in front of the Forbidden City, was later re-opened to vehicle traffic but no pedestrians were allowed near the site.
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