Harry Redknapp, the Tottenham manager, said: "We've closed the training ground. It's off limits. We're just going to train there and that's it.'
Prior to the midweek FA Cup replay against Bolton, Redknapp had warned that a virus had shown itself but, following the 4-0 win, it has taken hold.
"We had a few down with it the other day,' added Redknapp. 'Corluka had the virus and Palacios was not feeling great with it either.'
Following the visit of Everton, when Spurs can further improve their chances of getting into the Champions League, they face Fulham in the quarter-finals of the FA Cup, a week tomorrow.
Redknapp added: "It has swept through the academy. There are about 18 who work there or the kids who have all got it so the doctor decided we couldn't use it.
"It hasn't disrupted us, we are still training as normal and hopefully no-one else gets it but there have been so many other people who have gone down with it, including a few of the press boys who came over on Tuesday, it is certainly spreading."
Redknapp, who switched his normal pre-match press conference from the club's Essex headquarters to White Hart Lane, remains hopeful that Palacios and Corluka will be fit for selection against Everton.
A Spurs statement read: "A number of (academy) scholars and several first-team players have reported feeling unwell and, as a precaution, are being kept away from the training ground for a period of 48 hours in order to avoid the risk of spread.
"As an additional precaution, the club has undertaken a comprehensive deep clean of the entire training ground's facilities while all administrative and academy staff have been instructed to work from home until Monday."
It is not the first time Spurs have been hit by illness at a crucial juncture. Four years ago Tottenham needed to match Arsenal's result on the final day of the season but went down with a bout of food poisoning.
Attempts to have the final game, at West Ham, postponed failed even though 10 players were left with illness. Spurs lost 2-1.