Wright, on loan from West Ham at Nottingham Forest, did not mention Muscat by name in his column in the Sun but wrote: "He is a nobody. He knows it, I realise it and a hell of a lot of other people think it."
Muscat hit back saying: "He had a highly illustrious career but you would have thought he should have grown up.
"He kicked the ball away to get his first booking and then lashed out at me to get his second. He has only himself to blame - not anyone else. It was his ill-discipline.
"I'm told he has apologised to his manager and team-mates - and he should do. He has let them down."
Colin Lee, the Wolves manager, came to Muscat's defence. "I am a big admirer of Ian Wright's and for football's sake I don't want to see him getting sent off,' he said. "With all his experience and his tremendous attitude to the game I wouldn't have expected a little incident like this to spark off such a major reaction."
Wright's anger was sparked near the end of Sunday's 1-1 draw when Muscat allegedly shouted, prompting Wright to leave a ball that went straight to the defender.
Wright, already booked for kicking the ball into the stand after a decision had gone against him, had words with Muscat and then taunted him by peering at the back of his shirt in the pretence of finding out his name.
Three minutes from time Wright was sent off for a wild challenge that caught the Australian across the shins and was further irritated when his offer of a handshake was refused.
"I can sleep well and look in the mirror each morning, which is more than a certain Wolves player can probably do," Wright wrote.
"This guy isn't even worthy of mentioning his name. The unwritten code of gentlemen's conduct between players in these situations was broken and it sparked the worst kind of reaction in me.
"All it would have taken to sort the situation out was for him to say: `Sorry, I was out of order'. It would have been finished with. But this bloke is not big enough to do that."
West Ham's Joe Cole is battling to be fit for the England Under-18 international in front of his home crowd next month. He damaged his knee ligaments against Switzerland at Peterborough two weeks ago and the midfielder, who has yet to resume full training with his club, may even miss the vital European Championship qualifier against Spain on 6 October.
The game is likely to be the group decider and, even if Cole is unfit, the Hammers fans should have plenty of home talent to cheer on. Midfielder Michael Carrick, goalkeeper Stephen Bywater and defender Ezomo Iriekpen are all in the squad to face the Swiss.
England's other group matches should be relatively straightforward affairs and they play Cyprus at Brisbane Road on 8 October and San Marino at Dagenham and Redbridge on 10 October.
The group winners go into a two-legged play-off and whoever win that qualifies for next summer's finals in Germany.