Police are appealing for information on the attack, which took place on the canal path along the Aire and Calder Navigation, close to Birkwood Road, Normanton.
Two men, aged 82 and 74, were walking together along the canal path at around 9.30am on Wednesday, April 7, when two cyclists, a man and a woman, rode towards them.
It is reported that a short argument happened between the walkers and cyclists.
During this time, the male cyclist reportedly assaulted the two walkers by punching them and striking them with his bike.
The cyclists then rode away, and the two men were left with minor injuries.
Anyone who witnessed the incident or has information that could identify the cyclists should is asked to contact West Yorkshire Police on 101, quoting log number 356 of 07/04/21.
Alternatively, information can be given via the West Yorkshire Police live chat facility, or anonymously to charity CrimeStoppers on 0800 555 111.
Update, 5pm: A relative of the victims has now described the moment that the attack took place.