Snapchat footage of the players in their hotel room, allegedly filmed by one of the women, was released by Icelandic outlet DV.
Both players made their first Three Lions appearance on Saturday as England beat Iceland 1-0 in the UEFA Nations League.
According to The Sun, during their time in Reykjavik, the England team has been banned from seeing anyone outside their strict bubble, including family members.
Per BBC Sport, in a press conference on Monday, Southgate said: “Unfortunately this morning it was brought to my attention that two of the boys have broken the COVID-19 guidelines, in terms of our secure bubble.
“So we had to decide very quickly that they couldn’t have any interaction with the rest of the team and wouldn’t be able to train. Given the procedures we have to follow now they will have to travel back to England separately. Nothing has happened in the areas we occupy in the hotel.
“It is a very serious situation and we have treated it that way,” he added.
“They have been naive and we have dealt with it appropriately. I recognize their age, but of course, the whole world is dealing with this pandemic and there is a responsibility on all ages that they do their part.”
Southgate confirmed the pair had apologized for the incident.
Per the Press Association, Manchester City released a statement branding Foden’s conduct as “totally inappropriate” and “well below the standard expected of a Manchester City player.”
Similarly, Manchester United expressed their disappointment with Greenwood and said they are “liaising” with the FA.
Fans and writers took to Twitter to blast the players for their behavior following their first call-up to England’s senior side.
One said their conduct, especially given their debut status, is “beyond embarrassing,” while another said “The level of stupidity … blows my mind.”
As others observed, this incident is the last thing Southgate needed.
The Three Lions play again in the Nations League on Tuesday when they face Denmark in Copenhagen, but they will now do so without two of their most talented young squad members.