The arrests, made in an operation coordinated among the Police Corps, the Armed Forces of Malta and the Security Services, were the first break in the murder on October 16 that has drawn widespread outrage and condemnation.
The journalist focused her reporting for years on investigating political corruption and scandals, and reported on Maltese gangsters and drug trafficking.
Caruana Galizia, whose reporting focused heavily on corruption on the European Union island nation, was killed when a bomb destroyed her vehicle as she was driving near her home.
Regarding the way the Caruana Galizia family were informed, the Prime Minister said that he was informed that it was the inquiring magistrate, who had been pre-advised regarding the arrests, who was thought to be the one who would have given the arrests news to the family.
Operations took place in the areas of Zebbug and Bugibba, and the town of Marsa, according to Prime Minister Joseph Muscat.
"Caruana Galizia's critics called her a force of nature who had on at least one occasion nearly single-handedly brought the government to collapse". In the course of her investigations, Caruana Galizia accused several high-level Maltese officials of laundering kickbacks from wealthy Russians and Azerbaijani leaders - allegations those Maltese officials firmly denied. "Muscat ultimately won that election and with it, a second term".
A €1 million (US$1.2 million) reward was offered by the government for help in finding her killers. He was not comforted by vows from Maltese authorities that they would do their utmost to investigate the assassination.
Thousands of people have attended rallies demanding justice for the murdered journalist.
Muscat provided no other concrete information about the arrests or suspects, citing concerns that anything he says could derail any prosecution. Farrugia said he wouldn't disclose anything else because "I have been already threatened by legal action by the Caruana Galizia family". He said that the arrests resulted from a government investigation into the journalist's murder.
Muscat said earlier the suspects had been trailed for some time before the arrests were made.
A court hearing has been scheduled for Tuesday, when the police can officially file charges and the suspects can enter a plea.