J.A. van Plettenberg was born on the 8 March 1739 in Leeuwarden in Friesland, the Netherlands, the son of Hendrik Casimir and Agatha Petronella van Ammena. After studying law at the University of Utrecht, he left the country in 1764 to become a member of the Council of Justice in Batavia. In 1767 he married Cornelia Charlotte Feith.
In 1772 he came to the Cape Colony and succeeded Ryk Tulbach as the Governor of the colony in 1774. He resigned from this position in 1785 and returned to the Netherlands, where he died in 1793.
He was succeeded as Cape Governor by Lieutenant-Colonel C. J. van de Graaff.
Plettenberg Bay, on South Africa’s eastern coast, was named after the Baron in 1778 where he erected a beacon with the monogram of the Dutch East India Company, as well as his name.