The Football Association (FA) launched an investigation after the trio allegedly broke coronavirus protocols by attending a party, which reportedly was held to celebrate Abraham's 23rd birthday and took place at the Chelsea striker's London flat on Sunday (AEST).
Coronavirus regulations in the United Kingdom currently prohibit meetings of more than six people in social situations, but British tabloid The Sun claimed approximately 20 people were at the party.
The FA delayed Sancho, Abraham and Chilwell from joining the team while they looked into the incident and it has now been confirmed they will not take part against Wales.
Southgate added that they will not be in contention for Monday's (AEST) Nations League meeting with Belgium either if they are not able to join the squad on Friday.
"I think the players have already accepted they were in the wrong. They had broken those lockdown guidelines that were there," Southgate said.
"I have to be careful being on my moral high horse about things that happen when we aren't in camp with the team.
"We do have an issue in terms of the COVID guidelines and making sure any player that comes in is as lower risk as possible to the group. We are having to monitor the players, they are being tested today and tomorrow, we have to check for further symptoms.
"They obviously miss the game with Wales. If they are not able to be with us by Friday morning, they will miss the game with Belgium.
"We just have to make sure to protect the whole group - that is key. The timelines on the incubation period are really complex and we have to manage that as best we can."
Mason Greenwood and Phil Foden were sent home during the previous international break for breaching coronavirus protocols in Iceland and Southgate has reminded the players of their responsibilities.
"I don't think we can attribute what happens when they are the responsibility of their clubs to England," said Southgate.
"At the beginning of the week we had a good meeting with the players and spoke about the responsibility of being an England Player and how the spotlight is different.
"When the [Sancho, Abraham and Chilwell] story broke, there was no mention of their clubs. Whether they have one cap or 50 caps, it takes a lot of energy and time away from the team. The players in camp are 100 per cent focused on the game.
"If you are going into major tournament and it happens, then they can derail you. That did not happen in Russia and it allowed us to focus on our football.
"I have also talked about the connection of the fans and we have 10 with us who were in Russia. They have done good work with their clubs and communities, but some of the young ones have not done that and they need to prove themselves.
"They need to remember it is an honour to play for England. We have all made errors, I had nights out as player, but we are living in unique times with COVID. Politicians, businessmen have erred within the field.
"Fighting the virus, we need to work to pull together. There is a lot of disharmony now when before we saw people clapping the NHS and doing shopping for their neighbours."