Newcastle cruised to a 4-1 win over Hull City on Saturday, Moussa Sissoko scoring twice while Loic Remy and Vurnon Anita also found the net in a fine victory for the visitors.
But it was Pardew stole the headlines for all the wrong reasons in the 72nd minute when Meyler ran over to the sideline to take a throw-in.
Meyler shoved Pardew while retrieving the ball and the incident quickly boiled over with the visiting boss appearing to move his head forward and strike the former Sunderland man, who was booked for his part in the incident.
The Football Association have confirmed they will be looking into the incident, though the club have seen fit to move ahead and punish the 52-year-old themselves regardless.
A Newcastle statement read: "Newcastle United are disappointed with the actions of its manager Alan Pardew this afternoon (Saturday, 1st March).
"His behaviour was unacceptable and is not the behaviour we expect from the manager of Newcastle United.
"It is most disappointing that this incident has taken the focus away from what was a fantastic performance by the team and an excellent result away from home which leaves the club in eighth place in the Barclays Premier League.
"Sadly, the headlines tomorrow will not be focused on the result or the efforts of the players, but instead on the actions of our manager.
"Alan unreservedly apologised immediately following the game to the player, to Hull City Football Club and its fans, and to the fans of Newcastle United.
"We have held discussions this evening with Alan who has offered his sincere apologies to the club and it is clear he deeply regrets his actions.
"Alan has accepted a formal warning from the club in relation to his behaviour and also a club fine of £100,000.
"The club is now drawing a line under this matter and will be making no further comment."
