VIDEO: Eng, Scotland asked to explain tunnel fracas
Television footage appeared to show England back Owen Farrell and Scotland forward Ryan Wilson embroiled in some pushing and shoving before fellow players separated the pair.
Scotland went on to win the historic fixture for the Calcutta Cup 25-13 at Murrayfield.
"Six Nations Rugby will be writing to the unions to request clarification on what happened in the tunnel," a Six Nations spokesperson said on Sunday.
Once the unions have responded, tournament organisers will decide whether to launch an investigation or initiate disciplinary proceedings.
England coach Eddie Jones, along with players from both sides, denied any knowledge of the incident.
"I've been coaching a game. I've been pretty busy. Are you aware of it? You can show it to me after the press conference, then we can have a chat about it,"
Australian Jones quipped at the post-match press conference.
"In all seriousness, I don't know about it. If there was, we shouldn't let that detract from a great Scotland victory."
The incident was replayed at half-time in the match on British television and discussed by pundits.
Former England captain Martin Johnson had joked: "England's highlight so far I think", in reference to a dismal first half showing from the visitors, who trailed 22-6 at that juncture.
Agence France-Presse
Video: Raw Rugby