De Jong's sliding tackle slammed into Newcastle midfielder Ben Arfa's standing left leg in City's 2-1 Premier League victory on Sunday, leaving the Frenchman with a double break requiring surgery.
"Newcastle United FC have today written a strongly-worded letter to the Football Association in relation to the tackle," the club said in a statement on its website.
"The club has asked the FA for the appropriate action to be taken against De Jong for the tackle which in the club's opinion was unnecessary and used excessive force."
De Jong, who had already travelled to the Netherlands to join his national team, was excluded on Monday from coach Bert van Marwijk's squad for the Euro 2012 qualifiers against Moldova on Friday and Sweden four days later.
Manchester City manager Roberto Mancini gave his 25-year-old player his full backing on Tuesday.
"As his club manager I wish to say that whilst he is naturally competitive, Nigel is first and foremost a great player as well as being honest and loyal and I support him wholeheartedly," Mancini told the club website.
De Jong attracted criticism in July's World Cup final for kicking Spain's Xabi Alonso in the chest. The challenge earned him a yellow card only but English referee Howard Webb later said he wished he had shown a red instead.
De Jong's was not the only challenge to come under the spotlight at the weekend with Wolverhampton Wanderers captain Karl Henry shown a red card for a late lunge that sent Wigan Athletic's Jordi Gomez cartwheeling along the field on Saturday.
Henry apologised on Tuesday, saying he had deserved to be sent off in the 11th minute of the match which Wigan won 2-0.
"Having watched it again I can see that it looks horrific," he said on the club website. "I have already apologised to the manager... and the boys but I'd also like to apologise to the supporters."
