The 86-year-old man from the eastern Chinese province of Jiangsu is in stable condition in hospital in Taiwan, where he was on an eight-day tour, the Centers for Disease Control (CDC) said in a statement.
As many as 500 people may have had contact with him, all of whom are being asked to report to doctors should they develop possible symptoms, the statement added.
The 149 people who may have had close contact include two family members accompanying him on the tour, the tour guide, bus driver, medical personnel and patients sharing the same hospital ward, it said.
"Three medical personnel have shown symptoms of upper respiratory tract infections and taken medicines as preventative treatment," the statement said, adding that they should monitor their condition for two weeks while awaiting the outcome of tests.
They have not been placed in quarantine.
Taiwan in April reported the first H7N9 case outside mainland China, after a 53-year-old man who had been working in the eastern Chinese city of Suzhou showed symptoms three days after returning to Taiwan via Shanghai.
The Taiwanese government has issued a travel advisory for residents planning to travel to China, upgrading Jiangsu to "alert" level.
Guangdong province in the southeast has also been placed in the alert category.
An 80-year-old man infected with the H7N9 strain died on Thursday in Hong Kong, the first H7N9 death in the city since the virus emerged there last month.
He had been taken to hospital after returning to Hong Kong from the neighbouring city of Shenzhen in mainland China, where he lived.
Taiwan's CDC warned people to avoid touching and feeding birds or visiting markets with live poultry when visiting Chinese regions with H7N9 cases.