Taiwanese media broadcast footage of the clashes outside the Grand Hyatt, where Tsai is staying during her two-day US trip.
Opponents of Tsai -- many waving Chinese flags -- chanted slogans and fought with supporters, while one man was seen being detained and handcuffed by police.
Tsai is spending two days in New York ahead of a visit to diplomatic allies in the Caribbean.
Normally the head of a state passing through American soil would not spark controversy but Taiwan has long found itself in a precarious and unusual diplomatic situation.
The democratic island has ruled itself for seven decades but most countries do not recognize it -- including the United States, which switched diplomatic recognition from Taipei to Beijing in 1979.
Yet Washington remains its most powerful unofficial ally and biggest arms supplier.
China sees Taiwan as part of its own territory and has vowed to one day seize it, by force if necessary.
It bristles at any countries that might lend Taiwan diplomatic support or legitimacy.
"China is firmly opposed to official exchanges between the US and Taiwan," said Chinese foreign ministry spokesman Geng Shuang at a press briefing on Friday.
"We urge the US... to not let Tsai Ing-wen pass through its territory," he said, adding that the US should not provide a platform for "Taiwan independence separatist forces."
With the US currently engaged in a trade war with China, relations between Taipei and Washington have warmed considerably.
Unlike the last three American presidents, who were wary of angering Beijing, Donald Trump has ramped up relations with Taiwan.
Last week the State Department approved $2.2 billion arms sale to Taiwan, including battle tanks and anti-aircraft missiles, the first big-ticket military deal for the island in years.
Tsai transited through the US during a trip to the Pacific earlier this year, as well as last year's visit to Paraguay and Belize, both prompting official Chinese protests.
"Taiwan will not succumb to intimidation," her office said in a statement released as the US visit kicked off, without specifically mentioning China. "All difficulties will only strengthen our determination to go out to the international community."
On Thursday evening Tsai met with envoys from the 17 remaining countries that still recognize Taiwan.
She will attend a business forum on Friday and meet students on Saturday morning before heading to the Caribbean.
Tsai will visit Haiti, St Vincent and the Grenadines, St Lucia, and St Kitts and Nevis, which all recognize Taiwan.
China has poached five of Taipei's dwindling number of allies since Tsai became president in 2016.
Haiti has vowed to maintain ties with Taipei despite neighboring Dominican Republic establishing relations with China last year.
Taiwan pledged a $150 million development loan to Haiti, while Beijing reportedly offered the Dominican Republic investments and loans to the tune of $3 billion.