The square lies next to the Forbidden City, a former imperial palace and top tourist attraction, and was the location of pro-democracy protests in 1989 that were violently crushed by authorities.
In a notice to hotels, police identified two suspects and four car number plates, all from Xinjiang, in relation to a “major case” that occurred on Monday, the Global Times reported.
Police also instructed hotels to watch out for “suspicious” guests and vehicles, said the paper, which is close to the ruling Communist Party.
It carried the details in its English-language edition, but the Chinese version did not mention Xinjiang.
Security guards from several hotels in Beijing confirmed they had received a police notice.
A version posted online by 64tianwang.com, a Sichuan-based human rights news portal, gave the suspects’ names, identity numbers and registered residences, while urging hotels to report potential clues.
Its veracity could not be confirmed by AFP.
Xinjiang is home to ethnic minority Uighurs, many of them Muslim.
State media have reported several violent incidents there and a rising militant threat, but Uighur rights groups complain of ethnic and religious repression, while information is tightly controlled.
Police have arrested 140 people in Xinjiang in recent months for allegedly spreading jihad, and killed 22 Uighurs in August in an “anti-terrorism” operation, the official news agency Xinhua reported earlier.
One of the suspects named in the reported notice was from Lukqun, where state media said 35 people were killed in June in what Beijing called a “terrorist attack”.
China politics expert Willy Lam said the Tiananmen incident “looks like a terrorist attack” but cautioned that more information was needed.
“If it is indeed a terrorist attack it shows that Beijing’s efforts in trying to stamp out terrorism have not been very successful,” he added.
But Ilham Tohti, a prominent Uighur intellectual, said the police notice was not definitively linked to the Tiananmen crash, and even if a Xinjiang car was involved, it would not establish that members of the minority were responsible.
“Some media has suggested it was a terrorist attack carried out by Uighurs, without evidence being produced,” he told AFP.
“I worry that this event, even though it may have nothing to do with Uighurs, could lead local governments to increase repression and discrimination.”
Foreign ministry spokeswoman Hua Chunying declined to elaborate on the incident at a regular press briefing.
Newspapers mostly carried news of Monday’s crash low down on their front pages and in contrast to the Global Times used brief reports from state media – highlighting official efforts to control discussion of the event.
Chinese media outlets are known to receive instructions from the government directing their reporting of events deemed threatening by the ruling Communist Party, which in recent months has moved to tighten controls over all forms of media.
The state media reports, carried by all major newspaper and news websites, stressed official rescue efforts and did not contain information about whether the incident was deliberate.
Chinese social media sites, which are closely controlled albeit less strictly than print media, were an early source of pictures of the crash and speculation that it was an act of protest, but eyewitness accounts were rapidly removed.
The reports and witnesses said the SUV drove along the pavement outside the Forbidden City on the north side of the square before crashing into the crowd.
Images posted on Chinese social media sites showed the blazing shell of the car and tall plumes of black smoke.
China’s most popular Twitter-like service, Sina Weibo, employs thousands of staff in the northern city of Tianjin to delete politically sensitive posts, Chinese media have reported.
One eyewitness who posted photographs online told AFP that he had been contacted by Sina staff warning him not to post further information. The witness asked to remain anonymous out of fear of reprisals.
On Tuesday Weibo searches for “Tiananmen” and “bomb” returned a statement that “According to relevant laws and policies… search results will not be displayed.”
Searches for “Tiananmen” and “Xinjiang” did not produce any results posted after Monday.
The square appeared normal on Tuesday, with no sign of any damage at the crash site.
Residents of the Xinjiang capital Urumqi contacted by AFP did not report heightened security.