The prime minister said he would “of course” consider deregistering the union, which would strip officials of the right to enter workplaces and limit its ability to bring cases to the Fair Work Commission.
Both the union and the Labor opposition accuse the ABCC of acting as a political tool for the government.
Mr Morrison said it was wrong for Mr Setka to use his children for a political protest.
“The CFMEU has behaved under John Setka like a bunch of thugs and to involve his children in that, I think, is one of the ugliest things I've seen,” Mr Morrison told 2GB radio on Monday.
“When you see children being used in these sorts of protests ... this stuff just makes your skin crawl.”
Mr Setka has now apologised and deleted the tweet.
The union's national construction secretary Dave Noonan said he was not surprised the government had resurrected the CFMEU "bogeyman" to scare voters.
"When the Liberal Party is focused on good old-fashioned union-bashing, you know they're in trouble," Mr Noonan said.
"Any attempt to deregister the union will be vigorously resisted."
The prime minister said the actions of CFMEU officials reflected on Opposition Leader Bill Shorten because the union was a significant donor to the Labor party.
"You're known by who you stand next to," Mr Morrison said.
"Bill Shorten's got his arms all around John Setka, and John Setka's got his arms all around Bill Shorten."
Labor MP Michelle Rowland said the party did not endorse Mr Setka’s post. She said Labor could not be “tarnished” by association unless the Coalition was held accountable for the actions of its donors at the “top end of town”.
Additional reporting by AAP.