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Heinrich Rantzau or Ranzow (Ranzovius) (11 March 1526 – 31 December 1598) was a German humanist writer and statesman, a prolific astrologer and an associate of Tycho Brahe. He was son of Johan Rantzau.
He was Governor of the Danish royal share in the Duchy of Holstein, a rich man and celebrated book collector. Rantzau is perhaps best remembered as a patron of scholars. His own Tractatus astrologicus de genethliacorum thematum appeared in 1597, and went through five editions by 1615. In his own time, he was regarded as a generous supporter of artists and writers in Lübeck, many of whom he engaged to write memorials of his father. Rantzau was also a successful merchant with trading interests in the east-west trade through Husum and Lübeck.Rantzau was awarded the Danish Order of the Elephant in 1580 by King Frederick II of Denmark.
His oldest son Breide Rantzau was a councillor of the Danish realm, and a younger son, Gert Rantzau, was Captain of the castles of Kronborg and Flensburg.He was the great-uncle of Josias von Rantzau, Marshal of France.