The bird was spotted in the Catchwater Drain in Lincoln on May 2 and was reported to police by the Yorkshire Swan Rescue Hospital.
Lincolnshire Police said they believed the sock had been put on the animal deliberately because of “how snug the fit was and how far down the neck of the swan the tube was”.
However, a rescue charity said the swan and its partner were now both doing well and preparing for a new family. Roughly eight eggs are expected to hatch in about five weeks.
"They are very much together, very much in love, and are now planning for a family," said Dan Sidley, from the Yorkshire Swan and Wildlife Rescue Hospital which reported the initial incident.
He added: "We are really pleased with how this has turned out in the end."
It is an offence to kill or injure wild birds without a licence under the Wildlife and Countryside Act, and offenders can face up to six months in prison and an unlimited fine.
Lincolnshire Police are working with the RSPCA to ensure justice is served and investigations are still ongoing.
PC Llewellyn, Investigating officer at Lincolnshire Police, said: “Any type of animal cruelty will not be tolerated and we will carry out a full investigation into this incident. We work with wildlife organisations who report these incidents to us so we can investigate.
“We believe the item has been placed on swan’s head intentionally due to how snug the fit was and how far down the neck of the swan the tube was.
“We do not believe that this was accidental. Had the swan rescue not intervened, the swan would have either starved or potentially suffocated.
“We would like to hear from anyone who can assist us with our investigation or anyone who may have seen anyone around the swan in the water in the days leading up to May 2.”
RSPCA Inspector Kate Burris said: “The consequences of this mindless prank could have resulted in this poor swan suffering over a long period of time and ultimately ended in their death.
“Given that this is the breeding and nesting season at the moment this could have also resulted in suffering and sadly death for any dependent offspring.
“We would urge anyone who has any information as to who may have done this to this poor swan."
Anyone with information should contact police on 101 or the RSPCA cruelty line on on 0300 1234 999.
Yorkshire Swan & Wildlife Rescue Hospital received more than 5,000 calls about swans and other wildlife in 2020.
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