The soldiers, stationed at a checkpoint in Qalqilya, said they noticed the man coming toward them and holding a bag, ynetnews.com reported.
The soldiers ordered the man to stop after he pulled out the ax, but he refused, at which point one of the soldiers fired a warning shot into the air.
The man continued to approach them and was then shot in the foot. He was taken to a hospital in Jerusalem.
Maps and papers described as "nationalistic" were discovered inside the man's bag, police said, adding an investigation has begun.