Sunday's FA Cup tie between Wolverhampton Wanderers and West Bromwich Albion was interrupted by clashes involving the two sides' supporters that left many injured.
On Saturday, a spectator invaded the pitch at Vale Park and chased the referee off the pitch during a League One clash between Port Vale and Portsmouth.
Earlier this month, AC Milan keeper Mike Maignan faced racist abuse at Udinese, an incident that drew condemnation from FIFA president Gianni Infantino and many others.
In December, Luton Town striker Carlton Morris reported an alleged racist comment from the crowd during their Premier League game at Sheffield United, prompting a police investigation.
"Acts of discrimination, violence and entering the field of play are all criminal offences - which can result in individuals receiving criminal convictions, football banning orders and lifetime stadium bans," the joint statement said.
"While we understand that this behaviour is carried out by a small minority, we wish to remind everyone that these actions will not be tolerated."
They did not outline any new measures or punishments to prevent such behaviour.
The joint statement was also co-signed by the Football Supporters' Association (FSA), a representative body for soccer fans, and the UK Football Policing Unit (UKFPU).
"We will collectively work together, alongside the police, to bring offenders to justice and stamp this out of our game," they added.
