The Scottish SPCA is treating the injured bird after it was discovered by a member of the public in the north eastern area of Dumfries and Galloway, close to the Southern Upland Way.
If it had not been found, the bird was at risk of starving to death.
Environment minister Paul Wheelhouse condemned the shooting of the bird as "completely unacceptable".
Chief superintendent Mike Flynn, of the Scottish SPCA, told how the creature was unable to fly after it had been shot, leaving it unable to search for food.
He branded the shooting "cruel" as he appealed for anyone with information about what happened to come forward.
Mr Flynn said: "This eagle has been caused tremendous pain and suffering.
"It became grounded after being shot, which caused the feathers on its tail and wings to break and meant it was unable to search for food.
"If the eagle hadn't been found on Saturday, it is very likely it would have starved to death."
He went on: "Golden Eagles are extremely rare and it is very concerning that someone would deliberately try to injure or kill such a magnificent creature.
"As well as being cruel, injuring a wild bird is also a criminal offence under the Wildlife & Countryside Act 1981 and we are very keen to speak to anyone who has information about this incident."
Mr Flynn added that the eagle, which is now receiving specialist treatment and care at the Scottish SPCA's National Wildlife Centre, would require "lengthy rehabilitation".
But he said: "We are hopeful it will make a full recovery and we will be able to release it back into the wild next year."
Mr Wheelhouse said: "I am extremely concerned and disappointed that this golden eagle, a very rare sight in this part of Scotland, has been shot and critically injured. This is completely unacceptable.
"Shooting a protected wild bird is a criminal offence and I would urge anyone with information to contact the Scottish SPCA or Dumfries and Galloway Police.
"Thankfully, this Golden Eagle has survived and is receiving specialist care, and I hope in time it makes a full recovery."
There are 440 breeding pairs of Golden Eagles in Scotland.