About 600,000 Israelis live in over 230 illegal settlements built since the 1967 Israeli occupation of the Palestinian territories of the West Bank and East Jerusalem al-Quds.
The Israeli army sent reinforcements to the area on Wednesday and set up roadblocks near Palestinian villages. The gunshots reportedly came from a passing vehicle.
The settler, a 35-year-old rabbi, later died in hospital in Tel Aviv.
Israeli Prime Minister Benjamin Netanyahu issued a statement vowing Israel's security services "would do everything possible in order to apprehend the despicable murderer".
Occasional attempts by Israeli authorities to evacuate Havat Gilad have led to clashes with the settlers there.
Around 400,000 Israeli settlers live in the West Bank among some 2.6 million Palestinians.
Defence Minister Avigdor Lieberman called for the unauthorized outpost to be retroactively recognized in response to the attack.
The file of settlement expansion is the most prominent aspect of the Palestinian-Israeli conflict and one of the main reasons for the end of the last peace negotiations, sponsored by the United States between the two sides in mid 2014.
No group immediately said it was behind the shooting, but the Palestinian militant groups Hamas and Islamic Jihad praised the attackers. "Look no further to why there is no peace", Friedman said.
"In the aftermath of the decision to advance over 1,000 housing units in the occupied West Bank, I reiterate that Israeli settlement construction is illegal under worldwide law and is one of the major obstacles to peace", said Mladenov in a statement.
UN Mideast envoy Nickolay Mladenov also posted a tweet, both in English and Hebrew, condemning the attack.
"There is no justification for terror and those who condone it, praise it or glorify it". This is not the path to peace! At least one terrorist had opened fire on his auto from a moving vehicle near the Jewish community of Havat Gilad. Some mourners yelled "revenge" at the ceremony during a eulogy by Naftali Bennett, leader of the pro-settler Jewish Home party.
Palestinian Foreign Minister Riyad Maliki criticized the USA government on Wednesday for "giving the greenlight" to Israel, to do "whatever it wants with Palestinian land", with regard to Israeli announcements of plans to build over 1,000 new illegal settlement units in the occupied West Bank.
The Palestinians want these areas - along with the Gaza Strip - for the establishment of a future Palestinian state.