Humberside Police confirmed it has received no complaint from Meyler or the Tigers and are happy to let the Football Association deal with the matter.
The FA confirmed on Monday afternoon that Pardew, who has already been fined £100,000 and given a formal warning by his club, has been charged.
"Due to the serious violent and/or aggressive nature of the reported behaviour this case has been designated as non-standard," the FA said in a statement, the wording of which leaves them open to impose a ban beyond the usual guidelines.
Pardew has until 6pm on Thursday to respond to the charge - though he will at least be relieved not to be dragged up in front of magistrates.
Chief Inspector Rich Kirven of Humberside Police said: "We have been working with the FA and the football club to progress the matter appropriately.
"Having reviewed the circumstances of the incident, it has been agreed that the matter will be dealt with by the FA rather than considering any criminal proceedings.
"There has been no complaint received from the player involved or Hull City Association Football Club at this time.
"Whilst we appreciate that some people may have found the behaviour displayed at the game on Saturday offensive, Humberside Police will not be taking any further action."
Pardew was sent to the stands by match referee Kevin Friend after clashing with Meyler after the player had collided with him while chasing a ball into touch during Newcastle's 4-1 Premier League victory at the KC Stadium on Saturday.
The 52-year-old apologised after the game, but seems certain to face a very long ban indeed since it is not the first time he has been in hot water over his touchline behaviour.
He served a two-match touchline ban for shoving a referee's assistant on the opening day of last season, while earlier in this campaign he verbally insulted Manchester City manager Manuel Pellegrini.
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- Humberside Police