The Occupied Territories Bill was first introduced by a senator in January, but was delayed at the request of Ireland's minority government, headed by the Fine Gael party, which does not support it despite denouncing Israel's settlements policy.
Besides Israeli settlements, the bill also forbids imports from the Crimea and Western Sahara.
Students for Justice in Palestine (SJP) have welcomed a Seanad vote in favour of the Control of Economic Activities (Occupied Territories) bill.
Senior Palestinian Authority official Saeb Erekat hailed it as a "historic" vote and a "courageous gesture", which "sends a clear message to the global community and in particular to the rest of the European Union - to speak of a two-state solution is not enough without concrete measures".
"The Irish Senate has given its support to a populist, unsafe and extremist anti-Israel boycott initiative that hurts the chances of dialogue between Israel and the Palestinians; it will have a negative impact on the diplomatic process in the Middle East", the Foreign Ministry said in a statement. Those trading with Israeli settlements are complicit in the systematic denial of the Palestinian right to self-determination.
Knesset members had mixed reactions to the passage of the bill.
Al Tamimi was critical of other countries' lack of action on the subject, calling it a "shame" that "Ireland was forced to take this first step alone, as the European Union seems more interested in appeasing Israeli colonialism and oppression than in defending the rights of Palestinians". "On behalf of the government I am unable to agree that this bill is the way forward", Foreign Minister Simon Coveney said during the discussion that preceded the vote.
Israel has acted angrily to such moves in the past, heavily criticising the European Union after it backed labelling products produced in its settlements in 2015.
The legislation now faces eight stages that include a committee meeting and a vote in Dáil Éireann, Ireland's House of Representatives.
In the U.S. Senate, a bill doing the opposite has been proposed.
The bill only targets products made beyond the Green Line. It becomes law only with the signature of the Irish president.
The UK Government has formally objected to the erasure of Khan Al-Ahmar, supporting the position of the United Nations that settlements are illegal under global law, but has been criticised by Labour for offering nothing in the way of concrete actions to back up this objection.
On Tuesday, the Palestine Liberation Organisation urged Irish lawmakers to vote for the bill, the official Palestinian news agency reported.
Israel's Foreign Ministry has held the government accountable for the vote and has summoned Kelly to its offices for a Thursday meeting.
Kinvara has a tradition of supporting the Palestinian people.
The Ireland-Palestine Solidarity Campaign, which has been at the forefront of anti-Israel sentiment in Ireland, led to Israel banning some 20 activists associated with the Dublin-based group from entering the Jewish state as part of a "blacklist" by the Israeli government targeting anti-Israel BDS groups.