The Prisma store on Sakharova street was evacuated on the evening of June 3 after workers "noticed changes in local structural elements," according to a company statement.
Technical inspections are due to continue Monday to ascertain the nature of these changes and whether remedial work will be necessary.
"The shop remains closed and will be opened when it is completely safe for both customers and employees," the company said.
"There is no reason to suspect similar situations in other Prisma stores," it said, while adding that inspections would take place at all its other stores as a precuation.
Prisma Latvia is a subsidiary of the Finnish retail company S-group and operates four large supermarkets in Latvia.
The reaction of the company in immediately closing the store is no surprise. In 2013, 54 people lost their lives when a supermarket owned by the Maxima retail chain collapsed in the Zolitude district of Riga, with responsibility for the disaster partly attributed to shoddy and inappropriate construction methods and an inefficient evacuation procedure.
Criminal trials arising from the disaster are ongoing.