Foden was a notable absentee from Friday's training session due to illness, while Tomori and Guehi worked out inside the facilities after arriving at the Three Lions camp with injuries.
Speaking at his pre-match press conference, Southgate revealed that the physical problems would keep Tomori and Guehi sidelined, while Foden has now returned a positive COVID-19 test.
"Fikayo and Marc Guehi both arrived with injuries but they're progressing well. They won't be involved in tomorrow's game but there's a chance of involvement against Germany," Southgate told reporters.
"Phil Foden unfortunately has tested positive for COVID so he's had to leave. Hopefully he'll be able to meet up when we come back from Germany."
Foden's Manchester City teammate Raheem Sterling has also emerged as a doubt for the contest after picking up a bug, but it is unknown if the attacker is also suffering from coronavirus.
"Raheem Sterling has missed a couple of days training with a bit of an illness so we'll assess whether we involve him tomorrow, but everyone else is fully fit," Southgate added.
England's clash with Hungary at the Puskas Arena was originally expected to be played behind closed doors, with the home crowd targeting the Three Lions' players with racist abuse back in September's World Cup Qualifying clash.
However, a loophole in UEFA's rules means that children and guardians will be permitted to attend, and Southgate has called for education for the younger generation in attendance to avoid similar controversy.
"We've shown how we feel about these issues, in terms of racism and it's unacceptability. Hopefully the young people in the stadium will recognise why this opportunity has happened and in some ways maybe this will be part of the education for the next generation," Southgate said.
"Each generation that passes will bring more tolerance and we have the same situation in our country, so we've got to keep setting the right example. All being well, the young people will enjoy the game and take a bigger message from it."
Southgate was joined in front of the media by captain Harry Kane, who only needs one more goal to reach 50 for the Three Lions and close in on Wayne Rooney's all-time record of 53.
The Tottenham Hotspur talisman has outlined his intention to become the outright record holder "as soon as possible", saying: "It seems like a long time ago I made my debut.
"It's still one of the best feelings, playing for England and pulling on the shirt. Back then it wasn't a number I had in my head. It all goes so quickly with the games and major tournaments. It's great to be nearer 50, although still a few behind Wazza!
"I'd like to break it as soon as possible and see where we go from there. I don't let that stuff affect me on the pitch. It's not about records, it's about getting the three points and winning the game."
Following England's opener against Hungary in League A Group 3, the Euro 2020 runners-up take on Germany and Italy before welcoming Marco Rossi's side to Wembley to round off June's fixtures.