Toney has previously received racist comments on Instagram posts, and Brentford are now calling for more to be done after another case occurred.
"We are angered and frustrated to report that Ivan Toney has been subjected to racist abuse on Instagram once more," the Premier League club said in a statement on Wednesday.
"We have initiated investigations into this vile harassment, which we condemn in the strongest terms.
"Sadly, this isn't the first time Ivan has had to deal with this. A similar incident occurred just four weeks ago, leading us to identify an alleged perpetrator whom we reported to the authorities. To date, we have yet to see any action taken against that individual."
Brentford called for prompt investigations and criminal prosecutions.
"In general, the response from social media platforms to these ongoing issues has been underwhelming," the statement continued.
"Their solutions, such as filters to simply hide the abuse, may safeguard the players but miss the mark entirely and do not discourage the offenders. Without real consequences for those responsible, the cycle is doomed to repeat.
"We do have faith that things can change. We appreciate the dialogue that we have with the likes of Meta (which owns Instagram) but we call for more decisive and urgent action to combat online hate. We call for prompt investigations, and importantly, we call for criminal prosecutions."
The racism directed against Toney is the latest incident of abuse targeting players in Britain and in leagues across Europe.
Earlier this month, fans aimed monkey chants at AC Milan and France goalkeeper Mike Maignan during Milan's match at Udinese.
Coventry midfielder Kasey Palmer accused Sheffield Wednesday fans of doing the same towards him during their English Championship clash.
La Liga on Tuesday reported racist insults aimed at Real Madrid forward Vinicius Junior at Getafe's stadium to Spanish prosecutors.
