Under the policy, the US has formal ties with China rather than the island of Taiwan, which China sees as a breakaway province.
In a TV interview on Sunday, Mr Trump said he saw no reason why this should continue without key concessions.
China urged Mr Trump to understand the sensitivity of the Taiwan issue.
Foreign ministry spokesman Geng Shuang told reporters that the "One China" policy was the basis for relations with Washington.
China's hawkish Global Times tabloid dubbed Mr Trump "ignorant as a child".
"I fully understand the 'One China' policy, but I don't understand why we have to be bound by the 'One China' policy unless we make a deal with China, having to do with other things, including trade."
The US was being hurt by Chinese currency devaluation, tariffs, the building of a "massive fortress" in the South China Sea, and a failure to help over North Korea's nuclear ambitions, he told Fox News.
The comments come hot on the heels of Mr Trump taking a call from the Taiwanese president, who congratulated him on his election victory. It earned a rebuke from Beijing.
In Sunday's interview, Mr Trump remained defiant.
"It was a call, very short call, saying 'congratulations, sir, on the victory'... and why should some other nation be able to say I can't take a call?"
Taiwan: A pawn in Trump's chess game
The Trump phone call that will stun Beijing
Trump rejects CIA Russia hacking report
Rewind to 1949 and the Communist takeover in China. Kuomintang nationalists fled to Taiwan and set up their own government.
Since then, China has seen it as a renegade province, sometimes going so far as to threaten the use force if it ever declares independence.
After decades of formal diplomatic ties with Taiwan, the US decided in 1979 it was in its best interests to recognise the Communist government in Beijing as the sole legal government of China.
This was the result of years of warming ties between Washington and Beijing, starting with President Richard Nixon's celebrated visit in 1972.
Formal ties with Taiwan were cut, but strong informal links remain, including substantial military support.
So the "One China" policy is Washington recognising that there is only one China, and Taiwan is part of it. It is seen by many as ambiguous, but any suggestion that this could be changing raises hackles in Beijing.
Read more on the 'One China' policy?
The strength of China's displeasure depends on who you listen to.
Here's that Chinese foreign ministry spokesman again:
"China has noted the report and expresses serious concern about it. I want to stress that the Taiwan issue concerns China's sovereignty and territorial integrity, and involves China's core interests.
"Upholding the 'One China' principle is the political basis for developing China-US ties. If this basis is interfered with, or damaged, then the healthy development of China-US relations and bilateral co-operation in important areas is out of the question."
But the Global Times, which is linked to the ruling Communist Party, is somewhat firmer.
It suggests China may have to consider arming America's enemies or taking back Taiwan by force. The "One China policy cannot be traded", it warns.
"China must resolutely battle Mr Trump, only after a few serious rebuffs then will he truly understand that China and other global powers cannot be bullied."
He may be a businessman, it went on, "but in the field of diplomacy, he is as ignorant as a child".
China already formally protested to the US on 3 December over that phone call from Taiwan's president.
By way of contrast, on 7 December, China hailed Mr Trump's nominee for US ambassador in Beijing, Terry Branstad, as an "old friend" of China who could help advance relations.
Well it's not as if Donald Trump didn't tell us he was going to be tough on China.
Now, though, we are getting what looks like the outline of a strategy: the use of Taiwan as a bargaining chip.
It's a bold - some would say reckless - gambit, given that for China there is nothing vaguely negotiable about the island's status.
Mr Trump's team includes so-called "long-time friends of Taiwan" or China hawks who clearly understand the value of the island, at least as a bargaining tool in dealings with Beijing.
Some in Taiwan's administration feel his tough approach toward Beijing could enable Taiwan to build closer ties with Washington, its most important ally.
But many Taiwanese people are unsure if this approach will be good for Taiwan and question whether Mr Trump will truly stand up for Taiwan if conflict breaks out with China.
China says it is "seriously concerned" after US President-elect Donald Trump expressed doubts about continuing to abide by the "One China" policy.