Manchester City midfielder Foden, 20, and Manchester United forward Greenwood, 18, made their senior international debuts in Saturday's 1-0 UEFA Nations League win over Iceland.
Sources told ESPN that the team hotel was not exclusive to England and that Foden and Greenwood broke protocol by meeting the two women on the side of the hotel that was open to the public. England manager Gareth Southgate said the team area wasn't compromised because the women were not inside that part of the hotel. The FA found out in the early hours, and players were sent back to their rooms.
This prompted Southgate to omit both players from England's Monday afternoon flight from Reykjavik to Copenhagen, where they will play Denmark on Tuesday evening.
"Unfortunately this morning it was brought to my attention that the two boys have broken the COVID guidelines in terms of our secure bubble. They couldn't have interaction with the rest of the team," Southgate said at a news conference.
"Nothing has happened in the areas we occupy in the hotel. We are still getting the depths of the information. Still getting to grips with the detail. We have spent such a long time getting measures in place and the whole squad followed that to the letter.
"I'm not going into any more details until I'm clear of everything. No one from outside the hotel has been into the areas we occupy. We are very clear that no other members of our party have been in contact with the two players -- couldn't join us for breakfast or training. It is a very serious situation and we have treated it that way.
"I think at the moment I'm trying to take a lot of information in. Obviously they have been naive, we have dealt with it appropriately. I recognise their age, but the whole world is dealing with this pandemic."
Foden apologised for his behaviour to Southgate, the England team, staff and supporters on social media later on Monday, adding he was a "young player with a lot to learn."
"On this occasion I made a poor decision and my behaviour didn't meet the standards expected of me," Foden said.
"I breached COVID-19 protocols put in place to protect myself and my England colleagues. As a consequence I will now miss the opportunity to travel to Denmark with the squad, and that hurts.
"I will learn a valuable lesson from this error in judgment and I wish Gareth and the team good luck this week."
Iceland requires visitors to self-isolate for five days upon arrival. The Football Association negotiated an elite sports exemption to that rule following talks with the Icelandic government, but the team still had to stay in a bio-secure bubble for the duration of their stay.
Southgate's prematch virtual news conference was delayed by almost an hour as the FA launched an investigation into the incident.
Manchester United released a statement that read: "Manchester United are liaising with the Football Association and are disappointed with the actions of Mason Greenwood over this situation."
Manchester City were also critical of Foden in their response: "It is clear that Phil's actions were totally inappropriate.
"His behaviour not only directly contravenes strict guidelines related to COVID-19, but also falls well below standard expected of a Manchester City and England player. The club supports the FA regarding this incident."
Both players are expected to fly back to England within the next 24 hours.
Southgate also said there was no risk of the Denmark match being postponed.