Aufrecht was born in Leschnitz, Prussian Silesia, and was educated in Berlin, graduating in 1847, in which year he also published a treatise on Sanskrit accent (Bonn, 1847). With Kirchhoff, he collaborated in the publication of Die umbrischen Denkmäler (Umbrian memorials, 1849–51). With Adalbert Kuhn, he founded the Zeitschrift für vergleichende Sprachforschung (1852). In 1852 he moved to Oxford and studied at the Bodleian Library. From 1862 until 1875, he was professor at the University of Edinburgh in Scotland, where he occupied the newly established chair of Sanskrit and comparative philology. There, in 1875, he was granted the degree of LL.D.
In 1875 Aufrecht was appointed to the chair of indology at the University of Bonn, and remained at that post until 1889. Between 1891 and 1903, he published a three volume alphabetical catalogue of all Sanskrit manuscript collections known at the time, in a work titled, Catalogus Catalogorum. This was the first such attempt to catalogue all Indian manuscripts. Beginning in 1935, the University of Madras began working on an updated catalogue called the New Catalogus Catalogorum, a work that is still in progress.