Rau is the maternal granddaughter of former President Gustav Heinemann.

Her father was Eduard Delius (1921–2014), part in a long line of entrepreneurs in the textile industry of the Westphalian city of Bielefeld while her mother was Christa Heinemann (1929–2016), a daughter of the former President.

Through her mother, Rau is the niece of theologian Uta Ranke-Heinemann.

She attended boarding school in Switzerland (Hochalpines Institut Ftan) and the United Kingdom (Gordonstoun in Scotland, where Prince Andrew was a contemporary).

On 9 August 1982, she married Johannes Rau, 25 years her senior and a long-time friend of the Heinemann family, who was at that time the Prime Minister of the German state of North Rhine-Westphalia.