He was taught the rudiments of music and received his first piano lessons from his father, but was in large part self-taught.
Two years later, Louis Spohr heard him and arranged for a scholarship which allowed Kiel to study in Berlin with the renowned theorist and teacher Siegfried Dehn.
In 1866, he received a teaching position at the prestigious Stern conservatory, where he taught composition and was elevated to a professorship three years later.
In 1870 he joined the faculty of the newly founded Hochschule für Musik which was shortly thereafter considered one of the finest music schools in Germany.
Kiel's hobby was mountaineering and at age 60, he climbed Europe's second highest peak, the Monte Rosa, on the Swiss-Italian border.