No casualty or damage have been reported so far in the natural disaster. The 20 buildings reported damaged were mostly older structures, state media reported.
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Iran has experienced at least two other major disasters in recent years - one in 2005 that killed more than 600 people and another in 2012 that left some 300 dead.
During the night, early on December 13, a stronger quake of magnitude 6.0 struck the same area, the survey said. Tremors felt as far as the United Arab Emirates and Kuwait, Qatar, Turkey, Lebanon, Israel.
On November 12, a devastating 7.3 magnitude quake struck Iran in a region bordering Iraq, killing over 600 Iranians and injuring almost 10,000. President Hassan Rouhani has highlighted his government's efforts in bringing aid and temporary housing to the victims of last month's quake.