But the event, which could have helped create momentum for the gay rights movement in Japan, took place behind closed doors, with officials from the liberal council blocking reporters and putting their hands in front of cameras.
AFP reporters waiting to see her outside Shibuya City Hall were barred from getting near Conchita as she was guided into a van.
Shibuya's media blackout stood in marked contrast to the attitude of the Eurovision Song Contest winner, who tweeted in Japanese about her meeting with the mayor.
"Today I visited Tokyo's Shibuya City Hall, where the council decided to certify gay partnership as equal to marital status for the first time in Japan," she tweeted in Japanese with a photo of her meeting with the mayor. Soon afterwards she also wrote the same message in English.
The bearded lady's visit came after Shibuya assembly members voted to allow their officials to start giving out the "partnership" certificate for gay couples, the first such recognition of same-sex unions in Japan.
The certificate will carry only symbolic significance, since the Japanese constitution identifies marriage as a union based on mutual consent of the parties from "both sexes".
Shibuya officials say they will encourage hospitals and landlords to accept the certificate to try to ensure same-sex couples receive similar treatment to people who are married.
A city spokesman said there had been no intention to keep Conchita's rendezvous with the mayor a secret.
"Since it was their first meeting, the mayor wanted to see her quietly to build a trusting relationship for the future," he said.
Asked what the European celebrity and mayor Ken Hasebe talked about in the 30-minute meeting, the official said it was "just a casual greeting." "They also talked about how the new system came to a vote in the council," he added.
While Japan is largely tolerant of homosexuality, there is no specific legal protection for gay people, who complain that they may be prevented from visiting sick loved ones in hospitals or may be refused a tenancy because their relationship is not recognised.
Thursday's meeting came a day after around 450 people from sexual minorities appealed to the Japan Federation of Bar Associations to support their call to legalise same-sex unions.
Shibuya, famous globally for its "scramble crossing", is a liberal-leaning part of Tokyo and home to trendy cafes, bars and nightlife popular with younger people.