Speaking at a news conference, Southgate said they had both been isolated from the rest of the squad and would travel back from Iceland to Britain separately.
Video footage emerged of Manchester City’s Foden and Manchester United’s Greenwood allegedly meeting women in their hotel room after Saturday’s Nations League win in Reykjavik.
The footage came to light on Icelandic outlet DV after the women shared videos on Snapchat on Sunday.
“Unfortunately this morning it was brought to my attention that the two boys have broken the Covid guidelines in terms of our secure bubble – had to decide they couldn’t have interaction with the rest of the team,” Southgate said.
“We are still getting the depths of the information. Still getting to grips with the detail. I’m not going into any more details until I’m clear of everything.
“These are two boys I don’t know particularly well at the moment so I can’t speak in great depth. I have got to try and speak with them later in the appropriate way. They have got responsibilities and they have apologised,” he added.
Southgate also said that the right precautions had been taken while the team is still in Iceland so as not to put the Denmark game in Copenhagen game at risk.
Both players made their full international debuts against Iceland, 20-year-old midfielder Foden from the start and forward Greenwood, 18, as a substitute.
Like all of the England squad they were subject to strict Covid-19 health protocols to avoid Iceland’s quarantine rules.
These included not meeting anyone outside of the England squad and staff during the team’s stay in Iceland.
Foden apologised for his behaviour later yesterday, saying he would learn a valuable lesson from his “error of judgement”.
“I am a young player with a lot to learn but I am aware of the huge responsibility I have in representing Manchester City and England at this level,” he said on Twitter.
“On this occasion I made a poor decision and my behaviour didn’t meet the standards expected of me.”