Police believe the fire at a house in Parsonage Road, Withington, started in the living room at the back of the property at about 02:20 GMT.
Four children, aged between 10 and 17, and a man were also injured and are in hospital, the fire service said.
The man is in a serious condition after he was revived at the scene after suffering a heart attack.
Ch Sup Was Chaudhry said the children are being treated for smoke inhalation and compression injuries after jumping from a window.
He praised neighbours who helped rescue the family: "Without their help I'm sure other people would have suffered more serious injuries and possibly even fatalities."
One neighbour said he had heard people at the property screaming for help.
Mike Parr said he called 999 after he was woken by the fire, adding: "There was a huge amount of black smoke coming out of the house, quite a lot of flames."
Neighbours said a "quiet and polite" family lived at the address.
Student Emily Puckering, 22, said: "I could hear a woman, she was shouting and screaming... I could hear her shouting to the fire brigade, 'please save my house'.
"It's heartbreaking, it's absolutely tragic.
"I just feel a bit shocked. I just feel absolutely awful for them, for the family, for the children."
Formal identification of the bodies and post-mortem examinations are yet to take place, Greater Manchester Police said.
Officers are investigating the cause of the blaze in conjunction with the fire service.
Det Insp Tony Lea said: "My thoughts are with the family of the man and woman after such a tragic incident and we have specially-trained officers supporting the family at this time."
A man and a woman have died and five people have been injured in a blaze at a house in Manchester.