Scudamore said the decision had been taken following advice from police but said so far the nine other fixtures due to take place this weekend were expected to go ahead as planned.
“The very latest situation is that Tottenham and Everton has gone. The police have done a fantastic job, but it’s been a crime scene all week and the council have not had enough time to do what they need,” Scudamore said.
“The other nine fixtures are looking positive, subject to any more trouble.
“At 6pm tonight we will have a very clear picture. The Tottenham game is a real shame but we support the police in what they are doing.
“They want these games to go on as much as we do.”
Tottenham said the club had been powerless to prevent the postponement.
“Following ongoing discussions with the necessary authorities regarding this weekend’s Premier League home match against Everton, it has now been confirmed that this fixture will be postponed due to safety concerns relating to the infrastructure of the High Road and access to the stadium caused by last Saturday’s riots,” the club said in a statement.
“We apologise for any inconvenience caused to supporters due to matters outside of the control of the club. We shall update fans on when this fixture will be rearranged in due course.”
Spurs defender Michael Dawson expressed disappointment at the postponement but backed the decision.
“The most important thing is the safety of the fans,” Dawson said.
Tottenham was one of the worst hit areas in the rioting which rocked London for several days before a massive influx of police restored calm.
England’s friendly international against Holland on Wednesday had already been cancelled because of the violence, along with several other League Cup matches in London.