The 53-year-old was reportedly killed when the car she was driving exploded shortly after she left her home in Bidnija, near Mosta.
According to local media, one of her sons heard the blast and rushed outside.
PM Joseph Muscat, whom Daphne Caruana Galizia accused of wrongdoing earlier this year, denounced the killing.
“I condemn without reservations this barbaric attack on a person and on the freedom of expression in our country,” the prime minister said in a TV statement.
“Everyone knows Ms Caruana Galizia was a harsh critic of mine, both politically and personally, as she was for others too.”
However, Joseph Muscat stressed there could be “no justification… in any way” for such action.
“I will not rest before justice is done.”
On October 16, thousands of people attended a candlelit vigil in the resort town of Sliema.
Malta Television reported that Daphne Caruana Galizia had filed a complaint to the police two weeks ago to say she had received threats but gave no further information.
Police have opened a murder inquiry.
Newspaper reports said the explosion had left debris from the rental car she was driving strewn across the road and in a nearby field.
Daphne Caruana Galizia’s death comes four months after Joseph Muscat’s Labor Party won an election he called early because of the blogger’s allegations linking him and his wife to the Panama Papers scandal.
The couple denied claims that they had used secret offshore bank accounts to hide payments from Azerbaijan’s ruling family.
Daphne Caruana Galizia’s popular blog had also targeted opposition politicians, calling the country’s political situation “desperate” in her final post.
Malta has asked for international help – including the FBI in the US – to find the perpetrator, the spokeswoman said.
Meanwhile, Daphne Caruana Galizia’s family has requested that the magistrate in charge of the investigation be replaced, the Malta Independent reports.
It said the current magistrate had on a number of occasions been the subject of criticism by Daphne Caruana Galizia.
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