The ban comes days after Ireland, another small island with an open economy not known for its liberalism, voted overwhelmingly in favor of allowing same-sex marriage.
The MDA initially said that the song should not be aired on channels "that are freely accessed by younger viewers due to its mature content" but this was revised subsequently to include all cable TV and free-to-air TV channels, and TV or radio stations can be banned if they broadcast the song.
An MDA spokesman told the Straits Times newspaper that the song is allowed in Singapore for audio retail with the requisite consumer advice.
In a statement issued through her agent, Tsai said she had expressed her support for marriage equality through her music, and that while it was "a pity" that the song featuring same-sex marriage has been banned in the city state, she would respect "different views".
According to the Shanghaiist website, the song is based on a true story about a lesbian couple who were together for more than 30 years. When one was hospitalized due to old age and required emergency surgery, her partner was unable to give consent because she was not her legal spouse or family member.
Last year, Tsai's fellow Taiwanese singer A-Mei was told she could not sing her LGBT anthemRainbow at her concert in Singapore as that would breach the city-state's rules.
Taiwan has been one of the more progressive places in Asia in building support for the legalisation of same-sex marriage on the self-ruled island.
Legendary Taiwanese producer Li-Kong Hsu, who produced Ang Lee’s breakthrough movie The Wedding Banquet, recently backed another controversial film with a gay theme called Baby Steps, which deals with a gay couple trying to have a baby by surrogate.