Footage on social media showed a group of supporters breaking through security barriers and attempting to gain access to the stadium.
Thousands of fans have been peacefully building up to the game on Wembley Way since late Sunday morning, but scenes have become more violent as the 8pm kick-off approached.
Sam Wallace, a reporter for the Telegraph tweeted: "Just seen another fan jump down a 20 foot+ wall to try to get into the inner cordon near the media entrance.
"He’s telling the stewards escorting him away he had his ticket stolen."
Dominic King, a reporter for Daily Mail, tweeted: “There have just been two separate incidents of crowds trying to storm into the stadium.
“Wembley Way doesn’t have the kind of atmosphere you would want on an occasion such as this.”
Wembley Stadium spokesperson said: “There was a breach of security and a small group of people got into the stadium.
“We are now working closely with stadium stewards and security to remove these people. Anyone inside the stadium without a ticket will be instantly ejected.”
The Metropolitan Police made 20 arrests on Wednesday following England’s win over Denmark, with the group stage draw with Scotland seeing 30 arrests made.
Deputy Assistant Commissioner Laurence Taylor said ahead of the game: “The Met has a significantly enhanced policing operation in place and will adapt as necessary to the increased numbers of fans enjoying the match.
“We will continue to deploy a great many officers and specialist units to prevent crime and disorder and respond to any incidents right across London.
“We want people to be able to enjoy the Euros 2020 final safely and securely, behave responsibly and consider the safety and welfare of others.