The disturbing incident took place in the city of Piripa, Brazil, just 26 days after twins Anne and Analu were born.
Local media reports their mother Elaine Novais heard a sound coming from the room the twins were in while chatting to a neighbour. She was horrified to find a their family dog attacking her daughters.
She managed to rip the dog off them and called a family friend who is a nurse to help the tots.
Mrs Novais, a council worker who had struggled to conceive for nine years, pulled the violent dog away from the twins, but it had already inflicted fatal damage on their abdomens.
She gave the girls first aid before they were taken to Maria Pedreira Barbosa Municipal Hospital, with doctors saying one of the girls was declared on arrival, whilst the other was in a serious condition.
Doctors tried all they could but could not save the second girl’s life.
The doctor at the hospital who was responsible for Elaine during her pregnancy said the mother had always shown adequate care for her babies.
The local council said in a statement: "Faced with this immeasurable loss, we express our condolences and sympathy with parents Elaine and Regis, and their friends and family in this moment of sadness and pain.
"May God comfort your hearts and give you the strength to transform all the pain of this irreparable loss into faith and hope."
The local authorities have said they do not plan to launch an investigation into the incident.
An unnamed family member told local media the dog - believed to be a Labrador cross - was normally docile
"We think that with the birth of the twins, the animal was left out in a way, and it no longer had the attention and affection of its owners provided before.
"That could have caused some kind of jealousy and led the dog to attack the children."
It is unclear what has happened to the dog after the attack.