It has just emerged visitors to the sites of the Archdiocese of Glasgow and the Archdiocese of St Andrews and Edinburgh were re-directed to pornography instead.
The Diocese of Aberdeen was also targeted by the group which is thought to be in Malaysia.
Church officials told the Scottish Catholic Observer the group has previously targeted the banking group HSBC and the Canadian military.
A spokesman for St Andrews and Edinburgh Archdiocese said: "Our website maintenance company are now working on fitting extra security to the site as swiftly as possible.
"Whether or not we were attacked because we are a Catholic site is not yet known, however it is worrying that at least two other Catholic dioceses in Scotland have also been attacked by hackers in recent weeks."
All the dioceses involved said they were increasing security on their websites.
