Pardew was sent to the stands during the second half of the Magpies' 4-1 victory at the KC Stadium for an astonishing incident on the touchline, with FA chairman Greg Dyke later confirming the governing body will investigate.
Dyke told Sky Sports: "Clearly it looks serious and we will investigate it, but I can't really say anything else at this stage."
Pardew clashed with Meyler as the Hull man attempted to retrieve the ball for a throw-in, with referee Kevin Friend booking the Tigers player and sending the Magpies manager from the touchline.
Pardew was recently reminded of his responsibilities by the Football Association following a foul-mouthed tirade towards Manchester City boss Manuel Pellegrini at St James' Park.
And it appears the latest incident will see him facing further disciplinary action from the authorities, although he attempted to quell the furore with an immediate apology and explanation.
Pardew told Sky Sports: "It was just a heat of the moment thing. Obviously I massively regret it.
"I think I am going to have to sit down from now on because that's about two or three incidents I have been involved in on the line.
"I didn't mean to do anything aggressive, but I did move my head forward and that's enough.
"It was just because of the situation, if I was on the other side of the line, that wouldn't have happened, perhaps it will teach me to sit down.
"It's a shame, because it took the gloss off a fantastic performance from us. That's really upsetting as well."
Pardew added in his post-match press conference: "He was right on top of me and I wanted to just ease him away from me but obviously I put my head in a forward motion.
"I want to apologise to him, everyone at Hull and obviously my own fans as well.
"I don't think it was a headbutt. It wasn't a motion that was quick.
"Sometimes when you're on the sideline like that you can get involved in a moment like that. It was an incident that just flared up all around me. I just wanted to get him away, but with the forward motion... you can't do that.
"Of course, I'm not stupid enough to accept there's going to be no punishment. I'll have to accept whatever comes my way.
"I believe my behaviour over the years has not resulted in too many fines and sitting in the stands, but this one probably will."
Reflecting on the match, Pardew said Newcastle set their team up to be fast on the break and felt they were terrific.
"It was a great performance, it is very difficult to know where to start," he added.
"We were in control, we got the early goal. The goalie (Tim Krul) had to make a magnificent save at 0-0 but after that, we were in total control.
"Every time we were on the break we looked like we were going to score.
"It's a great performance and I'm sorry for the players and our fans that I am going to take the headlines away from it, probably.
"I'm representing a big, big club here and I shouldn't be involved in stuff like that, so apologies to everyone concerned."