The surviving bird had an arrow stuck in its wing and a further two arrows were found in the water and on the bank.
The birds were discovered on Saturday at an estate in Kirkcaldy, Fife.
Scottish SPCA inspector Sarah Gregory said: “A female swan had been shot through the wing in a cruel and mindless attack believed to have occurred on Friday evening.
“The arrow narrowly missed her vital organs and spine. The swan underwent surgery at a vets and is now in the care of our National Wildlife Rescue Centre in Fishcross.
“She is doing well and we are hopeful she will make a full recovery.
“We are currently awaiting post-mortem results to establish the cause of the male swan’s death, so at this stage we cannot say for certain that he was shot.
“These swans are a pair who have been returning to the estate for several years and why anyone would want to injure or kill these defenceless birds is beyond all reasoning.
“The estate owners are assisting us with our enquiries and we are working with Police Scotland to track down the perpetrator.”
The birds were found at Wemyss estate off Standing Stane Road.
Pc Lindsay Kerr, a wildlife and environmental crime officer with the Fife Division, said: “Our investigation into this atrocious act is ongoing and I today appeal to anyone with relevant information to come forward.
“At this early stage of inquiry we cannot say for certain that the death of the male swan was deliberate, however we are keeping an open mind to the possibility that both animals were targeted in a single incident.”
Anyone with information is urged to contact the Scottish SPCA Animal Helpline on 03000 999 999 or Police Scotland on 101.