Is it possible for a Jewish tourist? Is there anything important I should know?
It is possible. You can get to Kiryat Arba by public transportation from Jerusalem (Egged central bus station, DO NOT take any Arab transportation from the old city), and you can get to the site in Hebron from Kiryat Arba, in an organized manner, under IDF/Police protection.
You may be able to find organized tours from Jerusalem or other central locations in Israel, ask the receptionist in the hotel you'd be staying at.
DO NOT go to Hebron on your own, especially if you're Jewish. While a "regular" tourist can probably go through the Palestinian areas without much trouble, Jews are known to have been extracted by the police (either the Israeli or the Palestinian, or both) due to them being in a life threatening situation in PA areas. For Israelis its illegal to enter the PA areas, for Jews who are not Israelis it may be legal, but definitely not safe.
The Wikitravel article is NOT a good source of information for traveling in the West Bank. It has no consideration whatsoever for the security threats in the area, for reasons far beyond me.