Forty-nine people were hurt in the incident - seven seriously - which happened outside a church on the outskirts of the main town, Funchal, on Tuesday.
Offering his condolences, Portugal's Prime Minister Antonio Costa wrote on Twitter: "My thoughts are with the family and friends of the victims. The government has provided medical support given the high number of victims."
Jean Faulkner, a member of the intercessors teams at Holy Trinity Church Funchal, told Premier she was shocked at the news of the tree collapse.
She said: "When something like this happens, you think 'Why at this particular time does this tree fall?' It's just so sad and so shocking, to have killed so many people and to have injured many people.
"Prayer is the key to help the hurts of these people. We pray for the staff in the hospital, which is very small and quite over-crowded. We pray for the nursing staff who will be dealing with people afterwards."
The Nossa Senhora do Monte festival in Funchal was celebrating the Roman Catholic Feast of the Assumption which marks the end of Mary the Virgin's life on earth.
Footage on RTP public television showed ambulance workers at the scene and workers using chainsaws to clear branches of the tree away.
Regional authorities are now investigating what prompted the huge oak tree to collapse. According to local media reports, it was more than 200 years old.
Ten people died at the scene, while a child died en-route to hospital. A woman later died in hospital. It remains unclear where the last victim died.
Three days of mourning for the victims has been declared by the head of the regional government of Madeira, Miguel Albuquerque. The President of Portugal, Marcelo Rebelo de Sousa has visited the site of the accident.
Click here to listen to Premier's Alex Williams speaking with Jean Faulkner at Holy Trinity Church Funchal: