The woman was treated for the effects of smoke inhalation after trying to save her birds in the blaze in the early hours of yesterday.
The aviary was destroyed by the fire in the garden of a house at Hill Place in Dalkeith, Midlothian.
It is one of a number of incidents in the Mayfield area of the town being probed by police.
In another incident, a tarpaulin was set alight adjacent to the wall of a house occupied by a family with two young children.
At the same Stone Place address, a wheelie bin was deliberately set on fire and placed against a car, causing £3000 worth of damage.
Police said it was a matter of luck that no people were seriously injured by the fires.
Officers have been carrying out door-to-door inquiries and checking CCTV footage.
They want to hear from anyone who was in the area between 3am and 4am on Saturday and who may have seen anything suspicious.
They are keen to trace two young men, both about 5ft 8ins tall and wearing hooded tops, who were seen near Stone Place at around 4am.
Detective Sergeant Stevie Bertram, of Police Scotland, said of the latest incident: "The owner of the aviary suffered from smoke inhalation after trying to save her birds. She had to be treated by medical staff at the scene and in addition to her physical distress she is distraught about the loss of the birds which she has nurtured for a decade."