Latvia, where many of the young women come from, has said the lack of co-operation from gardaí and Irish authorities is making the job of tackling the issue very difficult.
Now the Council of Europe has asked Ireland to take urgent action to amend the law to include sham marriages as a form of exploitation and give the gardaí the powers they need to intervene in such cases.
It is not illegal in Ireland to arrange marriages for money.
The only action the Government has taken is to give gardaí powers to object before such marriages took place when they suspect they may be sham, but this was struck down by the High Court last year, saying objections could only be made after the marriage took place.
Ireland was named as one of the main countries of destination for the Latvian trafficking victims, alongside Britain, Germany, and Cyprus.
A team from the Council of Europe visiting Latvia to evaluate how well the convention on trafficking was working was told of the difficulties with the Irish authorities in helping to identify and help Latvians trafficked for the sham marriages.
Two years ago the Latvian authorities asked Ireland to take action to stop these marriages, mostly conducted with Pakistani, Bangladeshi, and Indian men. Being married to an EU national means the husband can apply for a passport of an EU country.
Latvia changed its anti-trafficking laws, introducing a prison sentence of up to three years for the offence.
Last year Latvia helped 16 victims of these sham marriages, most of them having being exploited in Ireland. However, the Council of Europe group say they believe the number involved is far higher.
Figures released last year by the Department of Justice said that up to the end of Sept 2011, there were 553 applications for residency from non-EU nationals as a spouse of an EU citizen, a third involved Latvian or Lithuanian spouses.
The Irish Criminal Law (Human Trafficking) Act 2008 would be amended to come into line with the EU directive due to come into force this year.
The Department of Justice did not comment on the report or the complaints from the Latvian authorities.
A statement said that minister Alan Shatter said he was working closely with his counterpart in Britain on the issue and had asked officials to re-examine to draft amendments on immigration related sham marriages in the Immigration Residence and Protection Bill 2010 and the Free Movement regulations that transposed the EU directive into Irish law. The bill was currently before the Dáil and Seanad.