England players Ben Chilwell and Mason Mount are self-isolating after coming into contact with Scotland midfielder Billy Gilmour, who tested positive for COVID-19 on Monday, the Football Association said in a statement.
"The pair will be kept away from the rest of the England players and wider support team," the statement added.
England manager Gareth Southgate said it was not yet clear if the pair would be available for England's final Group D match against Czech Republic at Wembley on Wednesday (NZ time).
"We don't know at the moment. There has obviously got to be quite a doubt. There are still a lot of discussions and investigations going on behind the scenes.
"We just have to find out over the next 12 hours or so," he told a news conference.
Current UK regulations for people who have been informed that they have come into contact with someone who has tested positive are for them to be isolated for 10 days.
Midfielder Mount has started both England's games while left-back Chilwell has yet to feature.
Both players are teammates of Gilmour's at Premier League club Chelsea and were pictured embracing him at the end of Friday's 0-0 draw at Wembley.
The FA said the move was a "precaution at this time" and the decision had been made after consultation with Public Health England (PHE).
"The pair will be kept away from the rest of the England players and wider support team, pending further discussions with PHE," said the FA.
"The entire squad had lateral flow tests on Monday afternoon and all were again negative, as was the case with Sunday's UEFA pre-match PCR tests".
The FA said they remain in contact with PHE and are observing UEFA's COVID-19 protocols for the tournament.