In the first half of City's Premier League clash against Arsenal at the Etihad on Saturday, Aguero disputed a throw-in decision on the touchline which Massey-Ellis - who was awarded an MBE for her services to football in 2016 - was overseeing.
Aguero was not happy with Massey-Ellis' decision to award a throw-in to Arsenal, and argued the call before putting his hand on her shoulder as the pair began to walk back toward the halfway line.
The City forward was not punished by referee Chris Kavanagh, who could have elected to show Aguero either a yellow or a red card for touching a match official.
But Labour MP Dr Rosena Allin-Khan condemned Aguero's actions, quote-tweeting a video of the incident along with her own message stating: "Who does Aguero think he is? Completely unacceptable".
Who does Aguero think he is?
Completely unacceptable.pic.twitter.com/fJ7L6zI2bt— Dr Rosena Allin-Khan (@DrRosena)October 17, 2020
Piers Morgan also voiced his opinion on Twitter, writing: "Erm, what is Aguero doing here? And why wasn’t he sent off for it?"
City coach Pep Guardiola sought to downplay the incident following the game, telling reporters: "Come on guys. Sergio is the nicest person I have ever met in my life. Look for problems in other situations, not in this one."