But officials said the decision to lease it to McDonald`s was made because they needed to cover maintenance costs.
Mr Chiang`s grandson and others have voiced their concern over the commercialisation of the site.
McDonald`s opened the 100-seat McCafe in the lower storey of the villa, situated by the city`s West Lake tourist attraction, over the weekend.
The upper storey, also leased out by officials, houses a Starbucks outlet which opened a month earlier.
Chiang Ching-Kuo is the son of revolutionary figure and Taiwanese leader Chiang Kai-shek, who fled to the island in 1949 after the Chinese Civil War.
Chiang Ching-Kuo later become the leader of Taiwan in 1978.
Chiang Ching-Kuo and his family stayed in the villa from October to November, 1948, and it was designated a cultural heritage site by Hangzhou officials in 2003.
The move has been criticised by Chiang`s grandson, Taiwanese businessman Demos Chiang, on microblogging platform Weibo.
"I don`t understand, opening a McDonald`s in the villa... how exactly does that adhere to regulations on correct usage of cultural heritage sites?" he said in a post.
In 2000, Beijing saw a similar controversy when a Starbucks outlet opened in the Forbidden City.
It shut in 2007 after officials decided to merge and cut down the number of shops in the palace, following multiple protests over the years about the commercialisation of the site.
Shared history
Beijing Youth Daily reported that the decision to commercially lease out the villa was met with strong resistance, with more than 90% attendees at a public consultation in January voting against it.
Conservationists suggested that the villa be turned into a historical museum promoting China-Taiwan ties. One of them, Zhejiang University academic Zhou Fuduo, noted that the villa was a symbol of China and Taiwan`s shared history.
"We said that the villa`s sociocultural value outstrips its commercial value, but in the end our proposal was ignored," he told the paper.
But officials pointed out that the local government needed money to recoup the cost of maintaining the building throughout the years.
A spokesman for the Zhejiang local government, which oversees Hangzhou city, told the newspaper: "Chiang Ching-kuo stayed in this home too briefly and what is left is just the main structure, the interiors look nothing like they used to when the Chiang family was here... there is not much point in turning it into a museum."
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