Match referee Howard Webb confirmed he had seen the incident but acted on it at the time and has no reason to change his mind.
"Howard Webb has confirmed to us that he saw the incident at the time," said the FA's director of communications, Adrian Bevington. "Therefore, that prevents us from taking any other action under FIFA regulations.
"The matter is now closed."
The veteran frontman was in trouble in the last round of the Carling Cup, when a similar challenge on Grimsby's Justin Whittle prompted the latter to bust Shearer's lip later in the game.
But Weir was man enough to say after the game it was nothing more than two players trying to get the better of the other.