His grandfather, Johann Friedrich Meckel the Elder (1724-1774), was professor of anatomy and obstetrics in Berlin and surgeon of Empress Catherine the Great.
During the Napoleonic Wars (1813–14) he served as a volunteer physician in the Armed Forces of the Kingdom of Prussia under General Ludwig Adolf Wilhelm von Lützow (1782-1834).
After a period as a pathologist with his half-brother Johann Friedrich Meckel (the Younger) in Halle, he received a professorship in anatomy and forensic medicine at the University of Bern, a post he held until his death.
Albrecht August Meckel was married to Luise Johanne Wilhelmine Schmelzer (1796-1873), with whom he had three children.
His son Heinrich Meckel von Hemsbach (1821-1856) was also a physician and professor of Pathological Anatomy.