Shearer told The Sun last week that Kinnear's appointment undermined Alan Pardew and turned the club into a "laughing stock".
In an interview with The Times, Kinnear reacted angrily to Shearer's suggestions and claimed that the former England striker "hasn't got a clue".
"What Shearer says is diabolical," Kinnear said in his interview. "This is a guy who hasn't got a clue about coaching.
"The last game of the [2008-09] season he came up with the master idea of playing Damien Duff at left-back. Damien is one of the best left-wingers in the business, but can't tackle. And we went down with an own goal from Damien.
"Shearer keeps slagging me off. He is being disrespectful to me. I am entitled to fight back."
Since Kinnear re-joined the Magpies, managing director Derek Llambias has resigned from his role at the club.