He was born in Drammen as the son of Hagbarth Kiær (1829–1903). In 1909 he was appointed professor of paleontology at the University of Oslo, as the first in Norway to hold such a position. His most important publication was Das Obersilur im Kristianiagebiete.
Johan Aschehoug Kiær was the grandson of Hans Andersen Kiær and nephew of Anders F. Kiær and Hans Theodor Kiær, all businessmen. He was a first cousin of Elias C. Kiær and Frits Kiær.