They say in a statement that today's stabbing was apparently politically motivated, and that the 19-year-old Palestinian suspect is being questioned in custody.
The 42-year-old victim was in critical condition and taken to an area hospital.
The suspect was apprehended by civilians near the scene of the incident in the town of Yavne before police arrested him.
The incident came amid tensions between Israel and the Palestinians over Israel's placement of metal detectors at a sensitive Jerusalem holy site.