Kraft was born and raised in Nuremberg. It is known that in his youth, he visited Ulm and Strasbourg. Kraft is believed to have married twice, but is not known to have produced any children.
His masterpiece is considered to be the 18.7 meter tall (61 feet tall) tabernacle, that may be seen in the Saint Lorenz church of his native Nuremberg. The stone tower, which is supported by four figures was restored after being damaged during World War II. One of the supporting figures is a self-portrait by Kraft.
Kraft is believed to have completed all of his sculpting work in Nuremberg and its environs in Bavaria, between the years 1490 and 1507, working with only a small complement of two or three assistants. He is buried in nearby Schwabach. Many of his pieces are exhibited at the Nuremberg museum, the Germanisches Nationalmuseum.