The Football Association is investigating the party which was held to celebrate Abraham's 23rd birthday and had more than six people in attendance.
"On Saturday evening I arrived home to find a small surprise gathering had been organised for me with family and close friends to celebrate my birthday," Abraham said in a statement to Sky Sports.
"Although I was totally unaware this was planned, I would like to wholeheartedly apologise for the naivety shown by all for the organisation and attending of this gathering.
"I recognise that I have a responsibility both in my professional and personal life to honour and respect the guidelines and deeply regret that this took place. All I can do now is learn from it, apologise to everyone and ensure it never happens again."
Sancho, who was also in attendance at the party, has been absent from Borussia Dortmund training due to a "respiratory illness" but has tested negative for coronavirus.
He said he didn't know how many people would be at the gathering.
"I would like to apologise for breaking the government guidelines and although I was unaware upon arriving of the numbers attending, I take full responsibility for my actions," Sancho said on Monday via an Instagram story.
"I will make sure moving forward that I learn from this."
Gatherings in England are not to have more than six people in attendance under government guidelines to limit the spread of the coronavirus.
"We are in close contact with the English FA and representatives of the national team. We are aware that they are following COVID-19 protocols in line with UEFA. It would not be appropriate for us to add comment at this stage," Dortmund told Sky Sports.
Abraham, Chilwell and Sancho will not join their England teammates at St. George's Park on Monday while the party is investigated.
"However, as a precaution to understand if there is any risk to the wider group, the arrival of Tammy Abraham, Ben Chilwell and Jadon Sancho will be delayed. This is to allow time to gather further information of a social gathering that all three players reportedly attended over the weekend," the FA said in a statement.