Rescue efforts continued through the night and police have launched a criminal investigation.
Three of those killed were emergency workers who were helping people trapped when more of the roof came down.
The number of deaths makes this the former Soviet republic’s worst disaster since independence in 1991, Latvia’s main news agency says.
It is unclear how many more people could still be inside.
The cause of the collapse is unclear although reports say a garden was being constructed on the roof at the time.
The supermarket, which opened in 2011, is part of the Maxima retail chain.
“The police have started the investigation already,” said PM Valdis Dombrovskis after visiting the scene.
“The criminal process has started about violating building standards.”
Interior Minister Rihards Kozlovskis told Latvian TV it was “clear” there had been a problem meeting building regulations.
TV footage showed rescue workers using mechanical cutters to clear debris from the single-storey concrete and glass building. Cranes were brought in to remove slabs of concrete.
More than 60 soldiers were helping the rescue effort, the army said on its official Twitter feed.
The initial collapse happened just before 18:00 local time on Thursday, when the store was busy with customers.
Walls and windows also crumbled, leaving the shell of the building piled with rubble, witnesses said.
About 20 minutes later another part of the roof caved in, trapping rescue workers who were trying to reach survivors.
The rescue services believe a total of about 500sq m (5,300sq ft) of roof caved in, according to reports.
Witnesses said customers tried to run out after the first part of the roof collapsed but the supermarket’s electronic doors closed, trapping them inside.
LETA news agency said the collapse represented the largest loss of life from a disaster since the restoration of independence in 1990, worse than a fire at a nursing home in 2007 that killed 25.
Normunds Plegermanis, deputy head of rescue services, said emergency teams faced difficult conditions at the supermarket.
“Falls are happening from time to time… it is very dangerous to work inside,” he said.
Local media said the building had been awarded a national architecture prize when it was completed in 2011.
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