Taiwan vowed to fight China's "increasingly out of control" behaviour after El Salvador switched its allegiance to Beijing previous year.
Tsai held a hastily arranged news conference on Monday, after the Solomon Islands chose to establish ties with China.
China has been trying to poach allies from Taiwan, and Burkina Faso, the Dominican Republic, Sao Tomé & Príncipe, Panama and El Salvador have already cut ties with Taipei, Reuters reports.
Tsai said the people of Taiwan will remain united, even if Beijing tries to retaliate against the island's plan to buy new fighter jets from the U.S., or to shift people's attention away from the ongoing unrest in Hong Kong.
Taiwan's foreign minister, Joseph Wu, said Taipei would immediately close its embassy in the Solomon Islands and recall all its diplomats.
Taiwan and mainland China have been governed separately since they split amid a civil war in 1949.
Soloman Islands breaks ties with Taiwan after Chinese 'dollar diplomacy'
Since Tsai's election, China has pressured global corporations to recognise Taiwan as a part of China and successfully persuaded a half-dozen countries to swap allegiances, using generous aid packages to escalate pressure on Tsai's Democratic Progressive Party.
A task force formed by the Solomon Islands' Parliament recommended this month that the government switch ties and set up a diplomatic mission in Beijing.
"The findings reveal that Solomon Islands stands to benefit a lot if it switches and normalises diplomatic relations with PRC [People's Republic of China]", the taskforce said.
The severing of ties on Monday leaves Taiwan with only 16 diplomatic allies. The prime minister's office did not immediately respond to questions.
Wu accused China of luring away the Pacific ally before Taiwan's presidential and legislative elections with a clear attempt to sway the January polls.
The Solomon Islands government has yet to respond to Taiwan's statement but for now the Pacific Island nation has no diplomatic relations with either Taiwan or China. The nation has had diplomatic relations with Taiwan for 36 years, during which time it has received considerable financial support from Taiwan.
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