The call is believed to be the first such contact between a U.S. president or president-elect and a Taiwanese leader since the United States broke diplomatic ties with Taiwan in 1979.
While there was no immediate response from China, the call would likely anger the nation. China considers Taiwan as part of the large communist nation, while Taiwan's government says itself a sovereign nation.
A statement released by the Trump transition team said Tsai congratulated Trump on his election win and he congratulated her on her win earlier this year.
The transition statement said the two noted the close economic, political and security relationship between the two countries.
The White House was not told about the call until after it happened, a senior administration official told The New York Times.
Trump also talked by phone Friday with Afghan President Ashraf Ghani; Singapore Prime Minister Lee Hsien Loong; and the Philippies President Rodrigo Roa Duterte.
He also promised to have most of his Cabinet posts filled by next week, calling his nominees "tremendous people."
The president-elect made the statement in an interview aired on Fox News Friday, a day after naming Marine Corps General James Mattis as defense secretary, an appointment that will be made formal on Monday.
Vice president-elect Mike Pence was quoted Friday in a Wall Street Journal article as saying the Trump administration will focus on illegal immigration, abolishing and replacing Obamacare (health care reform signed into law during the Obama administration), strengthening the military, and filling the vacant post on the nation's Supreme Court.
"Washington, D.C., is going to get an awful lot done in a short period of time," Pence told the Journal.
Also Friday, two members of the New York City Council began an online petition, asking Trump to provide federal funds to reimburse the city for the increased security costs - $1 million a day - to protect his family.
Trump lives, and his transition team is working out of Trump Towers in Manhattan.
"We ask you to commit the necessary federal funds to reimburse New York for all costs of protecting you and your family, both before and after your inauguration as president of the United States of America," the petition said.
Police have used barricades and dump trucks filled with sand to help fortify the area around Trump's building.
The city has estimated, according to the petition, that the cost of security at the New York residence could reach $4 billion by the end of a four-year term.
On Thursday, Trump visited the state of Ohio on what he is calling a "thank you tour" to greet some of the enthusiastic supporters who turned out for him on Election Day.
Trump has not detailed where else his tour will go, but several other stops are expected in the coming weeks, in states that carried Trump to victory.
Also Thursday, he visited the Carrier air conditioner company in the Midwestern state of Indiana, after he and Pence, the current Indiana governor, wooed Carrier executives with $7 million in tax incentives to keep the jobs in the state, even as the company sends others to Mexico.
Trump vowed to keep other companies from leaving the country and promised if they do, their products would "be taxed very heavily at the border" if they try to then sell the goods in the United States.
"Companies are not going to leave the United States anymore without consequences. Leaving the country is going to be very, very difficult," Trump had said.
Carrier is owned by the industrial conglomerate United Technologies. It said earlier this year it was relocating its Indiana plant to Mexico to cut costs.
Carrier says factors in its decision to stay include financial incentives from Indiana and a promise from the incoming Trump administration to "create an improved, more competitive U.S. business climate."
This story first appeared on Voice of America & is reposted here with permission.