Captain McShane and USA international Williams had to be separated by team-mates in the 83rd minute of the game.
The incident was not seen by match official, but was caught on video. Both players have until Friday to respond.
Reading manager Brian McDermott has spoken to both players since the incident and taken disciplinary action.
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The Royals lost the game 2-1 to a late Adam Forshaw goal moments after Matej Vydra had missed a chance to win it for the visitors.
Speaking before the charges were confirmed, McDermott said his side must move on from the incident.
"Football is a high-octane game," he told BBC Radio Berkshire. "We all want to win and it's one of those things.
"It's a volatile situation when you lose in the last minute. We've had a chance to win the game and we don't take it.
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McDermott, who returned to Reading for a second spell as manager in December, refused to say he was "disappointed" in his players' actions.
"These things happen, we're all human beings," he said. "This is what life is about, there's a lot worse things going on.
"The boys will apologise. We know it's not right, but this is a sport where we're trying to get to that league above.
"It's happened and we have to deal with it the best way we can."
Reading players Paul McShane and Danny Williams have been charged with violent conduct by the FA following an on-pitch row in their defeat at Middlesbrough.