The investigative journalist was killed by a vehicle bomb near her home in Bidnija on 16 October.
Malta has a population of 400,000 and is the European Union's smallest state.
"During this operation, 8 persons were arrested" the statement said, adding that they faced "reasonable suspicion in connection with involvement in the murder" of Caruana Galizia.
The journalist focused her reporting for years on investigating political corruption and scandals, and reported on Maltese mobsters and drug trafficking.
Ms Caruana Galizia, (53), was murdered on October 16.
Her criticism was also levelled at Prime Minister Joseph Muscat and his aides, who she accused of being linked to offshore companies and payments from the government of Azerbaijan.
"It is of little comfort for the Prime Minister of this country to say that he will "not rest" until the perpetrators are found, when he heads a government that encouraged that same impunity", Matthew Caruana Galizia wrote in mid-October. Farrugia said he wouldn't disclose anything because "I have been already threatened by legal action by the Caruana Galizia family".
"Last month, her family had alleged that Farrugia had divulged confidential information that could hamper the investigation".
He later tweeted that two others had been arrested with police sources saying they were also Maltese.
As per Maltese law, police will now have 48 hours to interrogate the eight people before prosecuting them.
A court hearing has been scheduled for Tuesday, when the police can officially file charges and the suspects can enter a plea.
Europol, the European Union's police agency, sent a team of organised crime experts to help Maltese police investigate the assassination, joining the Federal Bureau of Investigation and Dutch forensic experts.
Latching onto a retweet by the government's chief spokesman that several suspects could be charged with Daphne Caruana Galizia's murder, her son has lamented the lack of information given to the family.
She was well-known in Malta as a journalist who ran a popular blog that doggedly reported claims of corruption among leading politicians.
Muscat said Monday of the slaying: "As I stated as soon as I learned about this barbaric act, we will leave no stone unturned to get this case solved".