The Manchester City striker was criticised for grabbing Massey-Ellis' shoulder during the first half of his side's 1-0 Premier League win against Arsenal on Saturday evening.
Aguero, who was making his first City appearance since June after recovering from knee surgery, appeared unhappy with the official's decision to award a throw-in to Arsenal.
The Argentina international went unpunished but the laws of the game state that any "physical or aggressive behaviour" against a match official is considered to be a sending off offence.
It is understood that Aguero will not face any further action from the FA as the match officials did not believe it was required.
Pep Guardiola, the City manager, played down the incident and insisted that any aggressive behaviour on Aguero's part would be entirely out of character.
"Come on guys. Sergio is the nicest person I ever met in my life," Guardiola said. "Look for problems in other situations, not in this one."
Aguero played 65 minutes on his return to the City side and had a hand in Raheem Sterling's decisive goal, which saw Guardiola overcome his former assistant Mikel Arteta.