One employee at the scene who declined to be named estimated around 40 workers in the building when it collapsed, though he was not sure about the number of customers.
Family members could be seen at the site attempting to call relatives who may be trapped by mobile phone, while scores of rescue workers at the scene sought to clear debris and get oxygen masks to victims.
An AFP correspondent witnessed four people being brought out of the rubble alive. The cause of the collapse of the Melcom Shopping Centre was not immediately clear.
President John Dramani Mahama issued a brief statement through his Twitter account.
“My prayers are with the workers, shoppers and others who are trapped in the rubble of the collapsed Achimota Melcom building,” it said.
Some time later another tweet from his account said he was suspending his election campaign ahead of 7 December polls due to the disaster.
Witness Ama Okyere told AFP that “I was very close to the mall because I was going to buy something, only for me to see the building coming down.
“I had to run for my life. I was so terrified. I believe there are lots of people trapped under this because this is a heavily patronised shopping mall in the area.”
Another witness said he heard a bang followed by the building falling in.
“I was on my way to school and all of a sudden heard a big bang and people shouting, only for me to see that the shopping mall has collapsed,” said another witness, John Owusu.
The building in the capital of the West African nation of some 20 million people includes a number of shops selling a variety of consumer goods.