He revealed Stoke have written an official letter of complaint to the Gunners and also sent copies to the Premier League and the Football Association.
The row surrounds Wenger's comments earlier this week accusing the Stoke centre-back of turning football into rugby.
The Arsenal boss was fuming with Shawcross in February after his horror tackle left Aaron Ramsey with a sickening leg break - an injury the Wales midfielder is still recovering from.
His latest attack on Shawcross came after he was incensed by what he claimed were more rough tactics from the defender during Stoke's 2-1 defeat at home to Tottenham last Saturday.
Wenger commented: "You cannot say it is football any more. It is more rugby on the goalkeepers than football.
"When you see the way Shawcross kicked Heurelho Gomes, how Robert Huth pushed Gomes in the goal, you cannot say that is football anymore."
Pulis said: "The club is desperately disappointed with the comments which Wenger has come out with, especially the comments about Shawcross. We think they are out of order and you don't expect it from a person of Wenger's esteem.
"The club will deal with it in the right and proper manner."
The referee in the Tottenham match, Chris Foy, was the same referee who officiated in Arsenal's match against Blackburn.
When the issue was put to Pulis he said: "To say he was doing it as a sidetrack to influence the referee, you've said it. I've just agreed with you."
Pulis continued: "He's entitled to his opinion. We've fought two world wars to be a free country. We've all got different opinions and we must let people say what they say. Whether you agree with it or disagree with it, that's a different matter.
"What he said about Ryan was very, very poor and the football club will take that matter up."
Pulis also revealed goalkeeper Asmir Begovic would be staying at Stoke. Begovic was reported to have refused to play against Shrewsbury in the Carling Cup in midweek and had been linked with Chelsea.
But Pulis said: "He's young and naive and he's had his knuckles rapped. People make mistakes especially when they are young. We'll do our damnedest to keep Begovic at Stoke City."
Source: Team Talk
Source: Team Talk