The council brought in the boycott in 2009 after the invasion of Gaza in which thousands of Palestinians were killed.
The Jewish Human Rights Watch (JHRW) claim this motion, and others like it, are anti-semitic and lead to Jewish people being attacked.
Last month the JHRW launched legal action against Leicester City Council and last week they lodged similar suits against local authorities in Gwynedd and Swansea.
In the next few days it plans to start suing councils in Scotland including West Dunbartonshire, Clackmannanshire, Highland, and Newry and Mourne in Northern Ireland.
JHRW director Jonathan Newmann told the Reporter: “The legal action is against motions that West Dunbartonshire Council made in the past in 2009, and which were reiterated in 2010 and 2011 considering a boycott of Israeli goods.
“We’re seeking a judicial review to have the motion quashed.
“We consider this motion and motions like it to be essentially a boycott of Jews. The council has given reasons that we don’t agree we with and we believe this to be persecution which the Jews have seen for a millenium in various guises.
“The boycott of Jews is centuries old and we are fighting against it in our time.”
A statement released by the group added: “It is not the responsibility of local councils in the UK to make foreign policy which is directly leading to the rise in anti-Semitic attacks against UK Jews.
“This is a proxy war which has no place in local councils in the UK. Such actions have only one aim: to intimidate and make the UK Jewish population feel threatened and unwelcome.
“These hate motions are completely unacceptable.”
A West Dunbartonshire Council spokeswoman said: “Following the Israeli invasion of Gaza in 2008/09 during which more than a thousand Palestinian’s lost their lives, councillors voted to boycott all Israeli goods – made or grown in the country. This boycott still stands.
“This boycott is directed at the Israeli government. The council supports all religions and none and any suggestion otherwise is wrong. We have not been made aware of any potential legal action.”