He was a grandson of the Reverend John Abernethy. He was born in Coleman Street in the City of London on 3 April 1764, where his father was a merchant. Educated at Wolverhampton Grammar School, he was apprenticed in 1779 to Sir Charles Blicke (1745–1815), a surgeon at St Bartholomew's Hospital, London. He attended the anatomical lectures of Sir William Blizard (1743–1835) at the London Hospital, and was employed to assist as "demonstrator"; he also attended Percivall Pott's surgical lectures at St Bartholomew's Hospital, as well as the lectures of John Hunter. On Pott's resignation of the office of surgeon of St Bartholomew's, Sir Charles Blicke, who was assistant-surgeon, succeeded him, and Abernethy was elected assistant-surgeon in 1787.