Justice Minister Bassam Talhuni, quoted by official news agency Petra, said that "anyone who uses social media to spread hate speech" would face charges.
"Certain acts of incitement to hatred could be defined as terrorist crimes... and we will deal with them in accordance with anti-terrorist laws," he said.
On Monday, hundreds of protesters took to the streets calling on the government to resign over its failure to prevent the murder of Christian writer Nahed Hattar.
A bearded assailant shot dead Hattar, 56, Sunday on the steps of a court in central Amman where he was facing trial for sharing an anti-Islam cartoon on social media.
His family says the authorities were warned of threats to Hattar's life, including from his assailant, and of personal attacks on social media but had failed to take action.
The interior ministry said Tuesday an unspecified number of arrests had been made in connection with incitement to "hatred and confessional discord" on social networking sites.
They included a social media user who set up a Facebook page campaigning for the release of Hattar's killer, who gave himself up to police at the scene and faces a charge of premeditated murder.
Protesters shout slogans and hold portraits of prominent Jordanian writer Nahed Hattar, who was shot dead the previous day outside an Amman court, during a demonstration in front of the prime minister's offices on September 26, 2016
Jordanian authorities vowed Tuesday to crack down on incitement to violence on social media, two days after the murder of a writer over which the government has faced public anger.
