"According to sources, Seychelles, Mauritius and Madagascar unexpectedly and without prior notice revoked the charter's overflight permits," Pan Men-an, secretary-general to the president, told a news conference.
"The real reason is that the Chinese authorities exerted intense pressure including economic coercion," he said.
China claims Taiwan is part of its territory and opposes the self-governed island's participation in international organisations and exchanges with other countries.
Lai was due to visit Eswatini from April 22 to 26 for the 40th anniversary of King Mswati III's accession and his 58th birthday.
Eswatini, formerly known as Swaziland, is among Taiwan's 12 remaining allies that still recognise Taiwan's claim to statehood, after China convinced others to sever diplomatic relations with Taipei in favour of Beijing.
A special envoy will be appointed to attend the celebrations in Eswatini on Lai's behalf, Pan said.