Bristol Rovers' Carling Cup game against Watford on Wednesday night has been postponed at the request of police.
The civil unrest that started in London at the weekend has spread to other parts of the country over the past couple of days, with trouble breaking out in Bristol.
Bristol City's match at home to Swindon was called off due to safety reasons on Tuesday and Rovers' Memorial Stadium will not now be able to stage their midweek fixture.
The police contacted Rovers to advise them to cancel and a new date will now have to be arranged.
Football League chairman Greg Clarke has also warned matches will be postponed this weekend if police resources are needed elsewhere to combat the riots sweeping the country.
"The police have to make these calls," he told Sky Sports News. "If they feel they have more important things to do than send officers to football grounds, we will support that decision.
"Our priority is to make sure the police are out there dealing with unrest on the streets. We want to keep our games going ahead but that is a secondary priority.
"We have to support the police and the government in making the streets safe, then after that we can think about, 'let's get our football games going ahead'.
"If they need to move police away from football games, we will cancel those football games."
While the Premier League will decide on Thursday whether this weekend's top-flight matches will go ahead, Clarke expects any disruption to the league programme to be short-lived.
He added: "We don't believe the situation will go on much longer, history tells us these things tend to peter out and we will make sure football games can go ahead as and when.
"We will make those decisions as and when and will have conversations with the police on a case-by-case basis. If there is civil disobedience in an area and there are football matches scheduled in that area, we will review the situation minute-by-minute with the police.
"I wouldn't over-emphasise the number of games we could potentially lose. I don't want to talk up the sense of hysteria.
"I don't know, none of us do, what will happen tonight and the night after that and the night after that. These things tend to peter out and we hope that when they do we can go back to normal.
"Our priorities have to be ensuring safety on our streets and when that is ensured - in the short term, as I'm sure it will be - football will carry on."