The heated confrontation saw the duo having to be pulled apart by other Villa players as they squared up in their own box.
Mings appeared to be frustrated with the winger for not tracking back and doing his defensive duties and the 26-year-old was seen to be screaming at El Ghazi as he walked towards him.
However, the Dutchman was not willing to back down either and they came face-to-face with the 24-year-old appearing to try and headbutt Mings.
Referee Mike Dean choose not to issue any cards to either player and instead opted to try and calm both players down.
And Villa captain Jack Grealish revealed that at the half-time break the pair put the issue behind them.
“They shook hands at half-time,” Grealish said.
“It was all in the heat of the moment.
“We all said: ‘That can’t be happening out there.’ We have to be in this together.”
And after the game Villa boss Dean Smith admitted he wasn’t worried about the spat and was content the players had dealt with the issue.
“I wasn’t worried about that,” Smith said.
“What I do know is the lads sorted it out themselves. I didn’t need to say anything. The players dealt with it.
“It went over the edge of what we want but the lads dealt with it discreetly.
“There’s a great togetherness in our dressing room.
“I didn’t think about taking him off. That’s the end of it as far as we are concerned. They shook hands and got on with it.”
The draw saw Villa move out of the relegation zone on goal difference, at the expense of Newcastle United, while West Ham moved up to eighth in the table.