Alex Iwobi and his Toffees teammates have been quarantined following reports that a player manifested symptoms consistent with coronavirus.
The Merseysiders now become the third Premiership club to put its entire playing squad in quarantine.
Arsenal and Chelsea announced similar measures on Thursday.
Everton management say the club is in regular contact with the player in question and is monitoring the wellbeing of all players and staff. Its training complex has also been closed down along with its stadium, Goodison Park.
The coronavirus epidemic is currently gripping the whole of Europe, with sporting events and football leagues across the continent’s top five leagues now cancelled.
The English Premier League became the latest league to join Ligue 1, La Liga and Bundesliga in following Serie A’s cue by suspending the league.