He was born in Kassel, Hesse, Germany, probably in 1819. Völkner was one of several missionaries sent to New Zealand by the North German Missionary Society. He arrived in New Zealand in August 1849. In 1852 he offered his services to the Church Missionary Society (CMS). He married Emma Lanfear, sister of a CMS missionary. Völkner was ordained a priest in 1861 and took charge of the CMS mission station at Opotiki in August that year. There he worked among Te Whakatohea, who built a church and a school for him. He went to Auckland during 1864 and again in January 1865. He was then warned by members of Te Whakatohea not to return to Opotiki.
Ignoring the warning, Völkner returned to Opotiki with fellow missionary Thomas Grace on 1 March 1865. Both were apprehended, and Völkner was hanged the following day by his own Whakatohea congregation in the Völkner Incident. He was taken down and decapitated, and his eyes were gouged out and swallowed by Kereopa Te Rau, a Pai Marire emissary. The Anglican church in Opotiki was named St Stephen the Martyr in memory of his death.