A mother and her seven-month old baby girl died on Friday when the woman jumped off a building with the child strapped to her back, emergency services said.

"The 24-year-old woman and her 7-month-old baby died side by side. Her husband said they were having marriage problems," said Percy Morokane, emergency management services spokesperson.

He said the woman went to the top of a ten-storey building in central Johannesburg, where she lived with her husband and child, at about 8am and jumped.

"The husband said they were having marriage problems, but were happy. He said he didn't think she would go this far. He is very traumatised," he said.

The husband and wife came to South Africa from Zimbabwe two years ago. The woman was a student at Johannesburg University.

Police are investigating the incident.