Watford are working with Hertfordshire Police to identify the "loathsome individuals" who posted online abuse towards Bournemouth midfielder Jefferson Lerma.
The two Sky Bet Championship clubs are challenging for promotion, with Bournemouth having won an ill-tempered match between the teams at the Vitality Stadium on Saturday.
Tempers had flared during stoppage-time of the Cherries' 1-0 victory, with a late brawl resulting in Watford's Joao Pedro and Bournemouth's Jack Wilshere both being sent off for second cautions.
The fracas was sparked by Pedro's late sliding challenge on Lerma, and subsequently saw both clubs charged with misconduct by the Football Association.
Watford highlighted abusive comments towards the Colombian in reply to a post on the official Championship Twitter account promoting the EFL's anti-discrimination campaign 'not today or any day'.
The Hornets said in a statement on the club's official Twitter feed "While @HertsPolice and ourselves will attempt to identify these loathsome individuals, let it be known that they are not welcome to support our wonderful club.
"We condemn their comments in the strongest possible way. #buzzoff".
Bournemouth offered their thanks to Watford's positive action.
"We are grateful for the support of @WatfordFC in condemning and reporting these unacceptable tweets," a post on the Cherries' official Twitter feed read.
Heading into the next round of Championship matches, Bournemouth sit eight points behind third-placed Watford.
