The incident started when Palestinian men opened fire on an army post, seriously wounding the soldier. Other soldiers returned fire hitting a Palestinian bystander, the army said. The men fled and troops were carrying out searches.
The 18-year-old Palestinian, Ihsan Abu Hamdiya, who the army initially said was one of the men, was seriously wounded and later died of his wounds in hospital.
Tensions run high in Hebron where about 90 Jewish families live in heavily fortified enclaves among 162,000 Palestinians. There was no immediate claim of responsibility for the shooting.
The death brought the overall toll since the 2000 start of the Palestinain uprising to 4804, including 3731 Palestinians and 998 Israelis.
It came on the eve of West Bank talks between Rice and Palestinian leader Mahmoud Abbas, who has demanded that militant groups respect a seven-month-old informal truce.
On Friday, Rice held talks with Israeli Prime Minister Ariel Sharon who "emphasised the need to pressure the Palestinians to halt terrorism," his office said.