Counterfeit Smirnoff vodka has been found on sale in Irish shops and pubs.
However it said that tests so far had not shown any harmful ingredients, although the vodka had a lower alcohol content than real Smirnoff.
FSAI chief executive Prof Alan Reilly said that analysis carried out on the counterfeit product had not identified specific food safety hazards.
"However the source of the alcohol is unknown and there may be contaminants in other batches," he said.
"Given we have no information as to when or where this alcohol originates from, it would be unwise for anyone to drink it," he said.
The counterfeit vodka was found on sale in the retail and pub sectors.
The FSAI was tipped off by the UK Food Standards Agency which is currently investigating counterfeit alcohol.
The fake Smirnoff is labelled "Produced in Ireland" whereas real Smirnoff states "Produced in the United Kingdom".
The quality of the printed labels is also inferior to those on real Smirnoff.
However consumers may have old bottles of Smirnoff vodka purchased over
18 months ago that will legitimately state "Produced in Ireland" as that was the case then so there's no problem with these.
The FSAI said it has warned outlets selling alcohol of the counterfeit vodka in circulation and told them to remove any implicated product from sale immediately.
It is working with Smirnoff-makers Diageo, the gardai and customers to determine the source of the fake vodka.
It contains 32pc alcohol instead of 37.5pc in the genuine Smirnoff.
Although this counterfeit alcohol has not been shown to be harmful,fake alcohol can pose a serious health risk.
Dozen of consumers died in the Czech Republic last year when lethal methanol went on sale labelled as a local alcohol brand.