Lieuwe van Gogh shares about one-sixteenth of the same genes and, according to the museum, he "loved the project straight away".
New technology played a big part in the project. A 3D printer was used to shape the cells, which were grown at a hospital in the US city of Boston, so that they resemble the artist's missing left ear.
Famously, iconic 19th Century artist Vincent van Gogh cut off his ear during a psychotic episode in 1888.
Innovative artist Diemut Strebe said she wanted to combine art and science. Strebe said: "I use science basically like a type of brush, like Vincent used paint."
The novelty exhibition is at the Centre for Art and Media in Karlsruhe until July 6 and is due to go on display in New York City in 2015.
At the current exhibition visitors can speak into the ear through a microphone.