The Hampshire County Men's Final between Southsea Waverley and Boscombe Cliff was held in Southampton on Sunday.
A Boscombe player squared up to an opponent after a dispute over "bowls etiquette", reports the Bournemouth Echo.
Other Boscombe players then conceded.
It meant Waverley retained the men's county champions title.
Waverley secretary Peter Aldridge said both clubs were "mortified by the behaviour".
He said he had been told by members who were present that the player, in his 30s, was hurt after the argument blew up during the final and a headbutt was attempted.
Mr Aldridge said: "Bowls has changed over the years - people do get excited but this was not acceptable.
"It doesn't represent the attitude of Boscombe Cliff and is not representative of the game."
Boscombe Cliff Bowls Club has declined to comment.
The sport's governing body in the county, Bowls Hampshire, confirmed there was an incident which resulted in a Boscombe player being "asked to leave the green" and the team conceding the match.
Secretary Spencer Kerley said: "I am awaiting statements from the two clubs and from the county officers that were present before inviting the county to consider what further action may be necessary."
A Hampshire Constabulary spokeswoman said it had not been reported to police.
A county bowls final was abandoned after an argument erupted when a player appeared to headbutt an opponent, who fell and broke a finger.