England’s Ben Chilwell and Mason Mount have to self-isolate as a precaution after coming into close contact with Scotland’s Billy Gilmour.
The pair were seen interacting with Chelsea team-mate Gilmour after Friday’s draw with Scotland at Wembley.
Gilmour has since tested positive for Covid-19 and will miss Scotland’s final group game against Croatia on Tuesday.
The entire England squad had lateral flow tests on Monday afternoon and all were negative.
Gareth Southgate’s side face the Czech Republic in their final Euro 2020 group game at Wembley on Tuesday.
In a statement, the FA said it would hold further talks with Public Health England (PHE) before taking further action.
“The pair will be kept away from the rest of the England players and wider support team, pending further discussions with PHE,” read the statement.
“We will continue to follow all Covid-19 protocols and the Uefa testing regime, while remaining in close contact with PHE.”