The 10-minute telephone call with Taiwan's leadership was the first by a U.S. president-elect or president since President Jimmy Carter switched diplomatic recognition from Taiwan to China in 1979, acknowledging Taiwan as part of "one China".
China's Foreign Ministry said it had lodged "stern representations" with what it called the "relevant U.S. side", urging the careful handling of the Taiwan issue to avoid any unnecessary disturbances in ties.
"The one China principle is the political basis of the China-U.S. relationship," it said.
The wording implied the protest had gone to the Trump camp, but the ministry provided no explanation.
Speaking earlier, hours after Friday's telephone call, Chinese Foreign Minister Wang Yi pointedly blamed Taiwan for the exchange, rather than Trump, a billionaire businessman with little foreign policy experience.
"This is just the Taiwan side engaging in a petty action, and cannot change the 'one China' structure already formed by the international community," Wang said at an academic forum in Beijing, China's Foreign Ministry quoted him as saying.
"I believe that it won't change the longstanding 'one China' policy of the United States government."
In comments at the same forum, Wang noted how quickly President Xi Jinping and Trump had spoken by telephone after Trump's victory, and that Trump had praised China as a great country.
Wang said that exchange had sent "a very positive signal about the future development of Sino-U.S. relations", according to the ministry's website. Taiwan was not mentioned in that call, according to an official Chinese transcript.
China's Taiwan Affairs Office also called the conversation a "petty" move by Taiwan that does not change the island's status as part of China. Beijing is resolute in opposing independence for Taiwan, it added.
Trump said on Twitter that Tsai had initiated the call he had with the Taiwan president. "The President of Taiwan CALLED ME today to wish me congratulations on winning the Presidency. Thank you!" he said.
Alex Huang, a spokesman for Tsai, said: "Of course both sides agreed ahead of time before making contact."
WAYWARD PROVINCE
Trump and Tsai noted that "close economic, political and security ties exist between Taiwan and the United States", the Trump transition team said in a statement. Taiwan's presidential office said the two discussed strengthening bilateral interactions and establishing closer cooperation.
China considers Taiwan a wayward province and has never renounced the use of force to bring it under its control. Relations between the two sides have worsened since Tsai, who heads the pro-independence Democratic Progressive Party, was elected president in January.
Chinese state media downplayed the possibility of a major blow-up in Beijing's relations with Washington as Trump prepares to assume office.
Influential state-run tabloid the Global Times said in an online editorial that if Trump really overturned the "one China" principle upon assuming office it would create such a crisis with China he'd have little time to do anything else.
"We believe this is not something the shrewd Trump wants to do."
China's official Xinhua news agency said Trump needed to know Beijing can be a "cooperative partner" as long as Washington respects China's core interests, including the issue of Taiwan.
"China and the United States are not destined rivals," it said in an English-language commentary.
Washington remains Taiwan's most important political ally and sole arms supplier, despite the lack of formal diplomatic ties, the irony of which was not lost on Trump.
"Interesting how the U.S. sells Taiwan billions of dollars of military equipment but I should not accept a congratulatory call," Trump said in another tweet.
Trump has eschewed tradition in other calls with foreign leaders since he won the U.S. election, prompting the White House to encourage him to make use of the diplomatic expertise and counsel of the State Department.
Trump adviser Kellyanne Conway said on CNN that Trump was "well aware of what U.S. policy has been" on Taiwan.
Administration officials said Trump's team did not alert the White House about the call ahead of time. The White House also said after Trump's call that "longstanding policy" on China and Taiwan had not changed.
Advisers to the Republican president-elect have indicated that he is likely to take a more robust policy toward China than Obama, a Democrat, and that Trump plans to boost the U.S. military in part in response to China's increasing power in Asia. However, details of his plans remain scant.
Trump lambasted China throughout the U.S. election campaign, drumming up headlines with pledges to slap 45 percent tariffs on imported Chinese goods and label the country a currency manipulator on his first day in office.
Earlier this week, Trump spoke to Pakistani Prime Minister Nawaz Sharif and praised him, according to the Pakistani leader's office, as a "terrific guy".
Islamabad and Washington have seen relations sour in recent years over U.S. accusations that Pakistan shelters Islamist militants who kill U.S. soldiers in Afghanistan, a charge denied by the South Asian nation.
Trump also invited Philippine leader Rodrigo Duterte to the White House next year during what a Duterte aide said was a "very engaging, animated" phone conversation. Duterte has openly insulted Obama, who canceled a planned meeting with him in September.
A statement issued by Trump's transition team made no mention of the invitation.
(Additional reporting by Valerie Volcovici, David Alexander, Yara Bayoumy, John Walcott, Arshad Mohammed, Eric Beech, Jeff Mason and JR Wu; Writing by Jeff Mason and Raju Gopalakrishnan; Editing by Nick Macfie)
