The incident occurred less than 10 minutes into the game when Grealish was in the Birmingham penalty area and a spectator in a flat cap ran on to the field and threw a punch from behind the visiting captain, striking him on the side of the head.
The intruder was quickly restrained by stewards as several other Villa players rushed in to confront him. He was led away by police, blowing kisses to the crowd as he left.
West Ham midfielder Declan Rice was quick to react to the incident, tweeting: "Absolutely disgraceful what just happened to Jack Grealish"
Former England defender turned Sky pundit Gary Neville called for Blues to be docked points over the attack on Grealish.
Neville tweeted: "The club are going have to take a huge punishment for this to act as a deterrent in the future . A Points deduction or Empty stadium for 10 games !"
West Midlands Police announced an arrest had been made following the incident.
A post on the force's official Twitter feed read: "ARREST: Following the incident on the pitch involving an attack on an Aston Villa player; a man has been arrested and en route to a custody block. Further details to follow."