Clashes between supporters broke out during the FA Cup clash between the Baggies and Wolves on Sunday afternoon.
The game had to be suspended after fighting broke out between rival supporters, that then spilled onto the pitch.
While the players were taken down the tunnel after the suspension, Bartley was seen removing his family from an area of the stands near where the violence was happening.
talkSPORT commentator at The Hawthorns Nigel Adderley said: "That's the area of the field where a number of the players' families are during the games, which explains why the players were going over to the area.
"One or two people are being wrestled to the ground by police and stewards, a policeman has had his helmet knocked off as he grapples with a supporter.
"It's all very close to the family stand here at the Hawthorns, and now Kyle Bartley has now gone across, he's pointing at members of his family and one of the stewards is going across to make sure they are being led to safety.
"He's now carrying a young child away from the situation, I think it could be one of his own children, he's got his child out of the stand and I think he's taking more children away from the scenes.
"Bartley is leading members of his family down the touchline, and they'll go down the tunnel to safety."
Co-commentator Dean Ashton added: "What a disgusting position to find yourself in as a player, to feel that you have to get your family and your young children out of the stand where there's trouble.
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"How is that not enough of a sign to the supporters to get back in your seats?"
Adderley then spotted another incident nearer to the press box which led to more children being taken away from the scenes.
"And now beneath us there is another problem developing," he explained.
"More fans are grappling and more young fans are being pulled out of the stand by concerned parents.
"This is absolute madness!"
Bartley did not return once the match resumed, after a suspension of more than 30 minutes, with Wolves leading 2-0.
They held on to win the match as the remaining 12 minutes were played without incident.