Having passed through the State colleges of Schleswig and Husum, Krichauff served three years as an apprentice at the botanic gardens in connection with the University of Kiel. In 1846 he matriculated at the University of Berlin, and passed first class at examinations in Kiel. As a result, he was allowed a stipend by the Danish Government to travel as gardener and botanist; but the war of 1848 prevented him from enjoying this privilege.
Krichauff went to South Australia in December 1848, and settled at Bugle Ranges in the Adelaide Hills, east of the city of Adelaide. For many years he was the chairman of the District Council of Macclesfield, as well of the District Council of Strathalbyn. He was elected to the South Australian House of Assembly for Mount Barker on 9 March 1857, but resigned on 12 March 1858. He was again elected to the House, this time for Onkaparinga on 5 April 1870, serving until 22 May 1882, when he resigned his seat to travel in Europe and America. After his return he was elected to the Assembly for the district of Victoria (8 April 1884), and continued to represent the constituency until his retirement from the House at the 1890 colonial election.
Krichauff briefly served as a Minister in May 1870, when he was Commissioner of Public Works for twenty days in Henry Strangways' reconstructed Cabinet. He was returned to the South Australian Legislative Council in June 1890 for the Southern District, holding the seat until 18 May 1894.