Icelandic DV media reported that the two players were visited by two women in their hotel.
“Unfortunately, this morning [it] My attention has been brought to our attention that two boys have violated COVID-19 guidelines regarding our safe bubble, ”Southgate told reporters on Monday.
“We had to decide very quickly that they could not interact with the rest of the team and would not be able to travel to train.
“Given the procedures we have to follow now, they will have to go back to England separately.”
England players have been asked to stay in a safe team bubble during Nations League matches.
Foden of Manchester City and Greenwood of Manchester United won their first matches on Saturday, with Foden playing a full 90 minutes while Greenwood came on as a substitute for striker Harry Kane in the second half.
According to Southgate, the players were removed from breakfast and training on Monday after they were found to have violated protocols, adding that there was no contact between any of the other team members.
“Nothing has happened in the areas we occupy in the hotel,” he said. “We are still getting deep into all the information because, like I said, it wasn’t until two hours before training that I caught my attention.
“No one outside our party entered the areas of the hotel that we occupied.”
He later added, “At the moment I am trying to take a lot of information. It was clear that they were naive. We dealt with it appropriately.”
“I think everything from now on, I realize their age but of course the whole world is dealing with this epidemic and there is a responsibility on every age group to make sure that they play their role in keeping each other safe and not spreading the virus.
“We certainly don’t underestimate the importance of trying to preserve that bubble like we did.”
England defeated Iceland 1-0 after a chaotic end to the match which saw Raheem Sterling scoring a late penalty before Birker Piernason missed a penalty for the home side in injury time.
England will also miss defender Kyle Walker on the trip to Denmark, who lost 2-0 to Belgium in the other group match, where he is serving a suspension for receiving a red card in Saturday’s match.
Manchester City said Foden’s actions were “totally inappropriate”.
A statement from the club continued: “His behavior is not only in direct contradiction to the strict guidelines regarding Covid-19, but it is also far below the level expected for the Manchester City and England international player.
“The club supports the Football Association in connection with this incident, and officials from the club are in contact now regarding Phil’s early return to the UK.”
CNN contacted Manchester United for comment, but did not immediately receive a response. In a statement sent to Manchester Evening News, the club said it was “in contact with the Football Association and is disappointed by Mason Greenwood’s actions regarding the situation”.