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 con-demned 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. If the eagle hadn't been found on Saturday, it is very likely it would have starved to death."
He added that the eagle, which is now receiving specialist treatment and care at the Scottish SPCA's National Wildlife Centre in Fishcross, Clackmannanshire, would require lengthy rehabilitation.
However, Mr Flynn 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."
Police Constable Andrew Wheeler, wildlife crime officer for Dumfries and Galloway Constabulary, said: "It is beyond belief why someone would want to harm such a rare and beautiful bird in this day and age.
"This investigation will focus on bringing those responsible to justice for this abhorrent crime."
There are 440 breeding pairs of golden eagles in Scotland.