Burge was not part of the squad for last Saturday's 2-1 defeat to Southend and was once again omitted when Vale went down 2-0 to Rovers three days later.
The 24-year-old used his Twitter account to express his frustration, explaining that he had tried to contact Vale and his no-show at the meeting, coupled with his subsequent social-media rant, has prompted the npower League Two club to take disciplinary action.
"This is an unfortunate situation and one which could have been avoided," chairman Paul Wildes told the club's official website.
"In relation to his use of social media, we asked Ryan to apologise for his statements on Twitter on Thursday and Ryan declined to do this.
"Although we note that Ryan has now issued something on his Twitter feed, this has come too late.
"Ryan has signed our social media guidelines, along with all players, and we simply cannot condone behaviour which brings the club's name into disrepute.
"This whole incident could have been avoided and the club was keen to work with Ryan on a resolution, but he decided not to take this option.
"This has been a highly disruptive incident for everyone at the club at a critical time of the season."