The party said it will conduct an investigation into historical social media comments made by Sahar Al-Faifi.
Ms Al-Faifi appeared in Plaid Cymru's party political broadcast for the general election, which aired on BBC Wales, ITV Wales and S4C on Thursday.
The party said it will not tolerate anti-Semitism or racism "in any form".
Ms Al-Faifa has been asked to comment and the posts have since been deleted.
In the broadcast, she said: "Activists, it's us," in a reference to Plaid's slogan for the election campaign: "Wales, it's us."Since the party election broadcast, Sahar Al-Faifi has been accused on social media of making anti-Semitic Facebook and Twitter comments between 2012 and 2014.
Plaid Cymru said: "We have taken immediate action to suspend the person in question. We will investigate all allegations.
"Plaid Cymru will not tolerate anti-Semitism, racism or intolerance in any form. That includes the appalling abuse the individual has been subject to. It is not a part of the Wales we want to build."
She has also appeared on broadcasts for BBC Wales discussing her faith.
ReportOn Thursday, Plaid Cymru posted a picture on Twitter of Ms Al-Faifi, who wears a face-veil or niqab, to promote the party election broadcast later that evening.
Plaid Cymru sent a tweet saying the post received "abusive I responses" that are "unacceptable and will not be tolerated."
The party's tweet continued: "We stand with Sahar and all Muslim people in Wales and beyond.
"Wales is rich in its diversity. We are all Welsh citizens. We are all equal."
Since I don' know the full details of the allegations , whilst Plaid are right to suspend Ms Al-Faifi,, it highlights the difference between how allegations of Anti-Sematism and Islamophobia are viewed
The abuse that Ms Ms Al-Faifi, has undergone since the broadcast has been truly appalling and I sincerely hope that if any members of a political party made such comments they should be dealt with severely.
Which brings me to
"The Labour Party has said it will not investigate a Welsh general election candidate's alleged role in a Facebook group with links to anti-Semitic comments.Like Sahar Al-Faifims Caroll may be completely innocent , although the evidence seems to be damning .
Maria Carroll was referred to the party by Welsh Labour following reports in the Mail on Sunday.
UK Labour has said Ms Carroll had not been accused of making anti-Semitic comments.
She said she had not seen the relevant social media posts.
The Facebook group, whose contents are only available to group members, was reportedly set-up in order to advise Labour members subject to internal party disciplinary investigation on how to defend themselves.
Ms Carroll said: "I joined that group when left wing members were being suspended from the Labour Party en masse to prevent them from voting in the 2016 Labour leadership election, for incidents as small as retweeting [former Green Party leader] Caroline Lucas.
"When the group took an anti-Semitic conspiratorial direction I left it."
Labour's former Peterborough Council candidate, Alan Bull, was reportedly a member of the closed Facebook group.
He withdrew as a candidate after acknowledging it was a "bad mistake" to share an article on Facebook in 2015 which suggested the Holocaust was a hoax.
Ms Carroll said she did not see the "horrific social media posts" by Alan Bull as "these posts were not made in the group" she was in.She added: "I've been an outspoken critic of anti-Semitism in our party, including calling out anti-Semitic abuse towards [former Labour MP] Luciana Berger and anti-Semitism denialism within our party.
"I've been blocked by anti-Semitic accounts as a result."
Welsh Labour became aware of the accusations against Maria Carroll after being approached by the Mail on Sunday on Friday night.Image copyrightGETTY IMAGESImage captionFirst Minister Mark Drakeford said the party in Wales acted "immediately" over the concernsIn a statement on Sunday, Welsh Labour leader and first minister, Mark Drakeford said: "I am of course concerned of reports on the actions taken by Maria Carroll.
"Welsh Labour acted immediately and referred these matters to the Governance and Legal Unit of the UK Labour Party for investigation.
"I have consistently made it clear that anti-Semitism has no place in our party or in Wales," he added.
UK Labour has since told BBC Wales it will not be investigating Ms Carroll as she did not make anti-Semitic comments herself.
A source said the party centrally had not received any complaints about Ms Carroll.
But in a statement on Sunday evening, Fiona Sharpe from Labour Against Antisemitism, attacked the party's stance.
"We call on senior figures within Welsh Labour, including First Minister Mark Drakeford, to demand that a full investigation be carried out immediately and urge Ms Carroll to step down ahead of the general election," she said."Ms Carol
The problem is that in these days political opponents can trawl the social media comments of others and make allegations base on historical comments which may be taken out of context.
This does not excuse anybody but people do change and particularly mature .
I am less worried what someone said ten years ago as a teenager , than what is being said now.
We must also condemn not only those who make such comments , but those in power who whilst they do not make outright racist outburst ,give succour to racist and we should beware of them