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.
"We are shocked by the poor jail conditions."