Rescue workers pulled at least six people from the rubble, one of them dead.
A police officer co-ordinating the rescue effort said more than 30 people were trapped.
Excavators were trying to remove the building's broken beams and concrete blocks.
Melcom Ltd, which runs Ghana's largest chain of retail department stores, said it rented the building in the suburb of Achimota and opened its store there about six months ago.
"This is a tragedy and we are concerned about those trapped," said Vitalina Adjimani, a Melcom official. "Our concern is not about the loss of property but it's about human lives."
Emergency officials said the collapse was likely caused by structural failure.
A spokesman for President John Dramani Mahama said he was cutting short a campaigning tour in the north of the country for December elections to focus on the rescue efforts.