An official from the public bath told Kyodo News agency the decision had been made to avoid making other guests uncomfortable.
"Even if it is traditional culture, a typical person cannot judge the context behind the tattoos," the official said.
The facility always denied people with tattoos entry, as some customers were scared of them.
Chief Cabinet Secretary Yoshihide Suga told reporters that the incident was concerning in light of the country hosting the 2020 Tokyo Olympics, the Associated Press reported.
"It is important to respect the cultures of foreign countries, considering we will host the 2020 Tokyo Olympics and expect many visitors ... to come to Japan."
The incident has been reported widely by Japanese media, and also appeared in coverage in Austria, Australia, and Canada.
Mrs Brewerton was still in Japan today , and a family member told he Herald she did not wish to be contacted by reporters.
In May, Kiwi woman Claire Nathan was turned away during a job interview with Air New Zealand because of her lower arm ta moko.
At the time, Air New Zealand said tattoos were seen as "frightening or intimidating" in many cultures, and they did not want to make their customers uncomfortable.