President Bashar Assad made the changes by decree, CNN said. Foreign Minister Walid Moallem, Defense Minister Dawood Rajiha and Interior Minister Mohammad Ibrahim al-Shaar remain in those positions.
The new prime minister, Riad Hijab, was formerly minister of agriculture and agrarian reform.
The Syrian opposition boycotted parliamentary elections held in May. The government says turnout was high and the result was an overwhelming show of support for the Baathist Party.
Violence continued in the country as the shakeup was announced, CNN said. Opposition groups said at least six people were killed in shelling by helicopters in northern Syria.
About 15,000 people have died since large protests against Assad's regime erupted last year. Iraqi Foreign Minister Hoshyar Zebari said his country is concerned about "spillover" across the Syrian border.
Syria has also acknowledged shooting down a Turkish military jet Friday, saying it was flying low and was well inside Syrian airspace and near the coast.