Christian groups attacked Muslim-owned shops in the northwestern town of Chilaw on Sunday in anger at a Facebook post by a shopkeeper, police said.
Security forces fired in the air to disperse mobs, but the violence spread to nearby towns where Muslim businesses were also attacked.
Sri Lanka has been on edge since the April 21 attacks by jihadist suicide bombers on three hotels and three churches which left 258 dead.
Police said a night curfew in Chilaw and nearby areas was relaxed Monday, but the social media ban was brought in to prevent incitement to violence.
"Don't laugh more, 1 day u will cry," was posted on Facebook by a Muslim shopkeeper, and local Christians took it to be a warning of an impending attack.
Mobs smashed the man's shop and vandalised a nearby mosque prompting security forces to fire in the air to disperse the crowd. A curfew was imposed from Sunday afternoon until dawn Monday.
The main body of Islamic clerics, the All Ceylon Jamiyyathul Ulama (ACJU), said there was increased suspicion of Muslims after the Easter attacks carried out by local jihadists.
"We call upon the members of the Muslim communities to be more patient and guard your actions and avoid unnecessary postings or hosting on social media," the ACJU said.
Internet service providers said they have been instructed by the telecommunications regulator to block access to Facebook, WhatsApp, Instagram and other platforms.
The latest unrest came as Catholic churches resumed their public Sunday masses for the first time since the bombings.
Sri Lanka has been under a state of emergency since the suicide bombings. Security forces and police have been given sweeping powers to arrest and detain suspects for long periods.
Muslims make up around 10 percent of Buddhist-majority Sri Lanka's 21 million population and Christians about 7.6 percent.