Private broadcaster TBS reported that a "considerable number" of people were feared dead inside the mall in the town of Kashima after the fire brigade said that the second floor collapsed in the 7.1-magnitude tremor.
Emergency services earlier said "many people" were trapped inside the building.
Public broadcaster NHK cited police sources as saying that between 20 and 30 employees could not be contacted, showing footage of emergency vehicles with flashing red lights outside.
Police told AFP they could not confirm any fatalities inside the building. Kyodo News reported that four people had been taken to hospital, all of them conscious.
Multiple people were also believed to be unaccounted for at a factory in Yatsushiro city where the tip of a chimney fell down, NHK reported, citing sources.
