Nurul Izzah said the conditions were inappropriate for her father, who she called a "political prisoner", and could exacerbate a chronic back problem and otherwise threaten the 67-year-old's health.
Anwar was jailed last week for five years by the country's highest court on a sodomy charge, likely ending his career in politics.
"My father is kept in a cell which is deplorable. It is a bare cell with a two-inch (5 cm) foam mattress placed on the floor, a bucket for bathing and a squat toilet," said Nurul Izzah, 34, an opposition member of parliament.
Anwar had led a rebirth of a once-downtrodden opposition that is threatening to unseat the regime that has been in power since independence in 1957.
His jailing has drawn international criticism including from the United States, which said it raised questions over judicial independence.
Anwar denies the sodomy charge, calling it a "political conspiracy" by the government to curb the opposition's momentum.
Nurul called on authorities at Anwar's prison near Kuala Lumpur to provide a hospital bed.
"We demand a proper bed, a table and chair as the sodomy case is politically motivated," she said.
Following his sacking, he was jailed for six years on sodomy and corruption charges.
That case was widely seen as politically motivated, and the sodomy charge was later overturned.
Anwar, however, was in "good spirits," during their family's first visit to see him -- through a glass panel -- last Friday, Nurul said.
"He told us not to cry. He cheered us by singing songs to his grandchildren," she said.
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