The incident, which occurred at around 1.45pm on Sunday October 13, involved two male suspects who were seen by a member of the public attracting the swan towards the River Don canal path in Mexborough.
One of the men then swung a piece of wood at the swan, hitting it in the head and killing it.
The two suspects are then believed to have left the scene heading towards the George and Dragon pub on Church Street.
CCTV stills released by South Yorkshire Police show two men who officers believe could hold information about the killing.
Anyone with information is advised to call police quoting crime reference number 14/155254/19, or call Crimestoppers anonymously on 0800 555 111.