In a group-wide email to its 232 stores nationwide, it stated that products originating from Israel were to be withdrawn.
"It's mostly fruit and vegetables, carrots and herbs more specifically," a source from the retailer told the Herald.
SuperValu is part of the Musgrave Group which includes 462 Centra stores around the country.
It is not understood if the withdrawal of the products extends to Centra shops as well.
The call to remove the Israeli products was made last Friday.
In the notice it said: "The above product (carrots) is being withdrawn from sale. There is no Food Safety or Quality Issue associated with this withdrawal."
The above statement was made in relation to the "nature of the issue".
The action advised was to "remove all stock from available sale and dispose of at store level".
The company also stated that "customer returns (on the product) should be honoured".
The circular was sent to all store managers and was effective from the date of receipt.
Musgrave is a family-owned business operating since 1876. Including its retailers it is Ireland's biggest private sector employer, with a staff of 60,000.
The group had not responded to requests for comment at the time of going to print.
Meanwhile, Irish and Leinster rugby star Gordon Darcy took part in a protest with 2,000 people supporting the people of Palestine. His Exchequer Bar was one of the first in the capital to ban the use of Israeli products.
And toy store Smyths had a poster in its Jervis Street window over the weekend stating that it had removed products made in Israel from the shelves.
When the Herald visited the city centre store the sign had been removed and staff said they would not be commenting on the matter.
A spokeswoman for the toy stores said: "One store last week took several products from one country off its shelves. This decision has now been reversed.
"We do not engage in national or international political affairs."