A man was arrested and another man taken to hospital following the incident during a training session for Kirkheaton Youth FC U9s at Leeds Road Playing Fields.
It is believed a dispute broke out between the two men concerning an incident involving two young players on the pitch.
A man in his 50s is then reported to have attacked the other before the fight was broken up and the police were called.
The incident was witnessed by young players and parents.
One parent said: “The kids saw everything.
“The kids were that upset that their parents had to take them home.
“Thankfully there was an off-duty police officer playing tennis nearby. He and a couple of guys broke it up.”
The parent added: “It’s disgusting. I’ve never seen anything like it before.
“My son was really upset – they all were.”
Kirkheaton Youth FC committee member Darrell Phillipson said: “At the moment we are getting all the evidence together to make sure this is all done properly.
“The club is taking this very seriously.”
West Yorkshire Police said a man in his 50s had been arrested on suspicion of assault and cautioned.