Riot police charged England fans in the centre of Porto after beer glasses were thrown in the special fanzone set up for the Nations League finals.
"The FA strongly condemns the scenes witnessed in Porto overnight. Anyone responsible for these disturbances cannot be seen as true England supporters and are not welcome in football," said the FA statement.
"They are an embarrassment to the team and the thousands of well-behaved fans who follow England in the right way. We are liaising with the UK Football Policing Unit."
England supporters were staying in Porto ahead of Thursday's match in nearby Guimaraes against the Netherlands and had gathered in the fanzone to watch Wednesday's match between Portugal and Switzerland on outdoor big screens.
The Guardian newspaper reported that hundreds of England fans were baton charged by riot police after they threw beer glasses.
Deputy chief constable Mark Roberts, the National Police Chiefs' Council football policing lead, said in a statement that the behaviour was "incredibly disappointing" and "completely unacceptable".
The FA last week urged supporters of the national team to stamp out “embarrassing” and anti-social behaviour.
They released a video called "Don’t be that idiot" to highlight examples of English hooliganism that had come to light in recent months.
The video ended with a message from England manager Gareth Southgate encouraging supporters to make the country proud by being on their best behaviour.
(Reporting by Simon Evans, editing by Nick Mulvenney)
