"For too long, you’ve been able to remain anonymous — able to skirt your financial and legal responsibilities with no shame," Ducey said in his State of the State speech Monday. "Not anymore."
Each photo that it tweets for those wanted will include the hashtag "#deadbeat," he added.
The state has already started, with the Arizona Department of Economic Security shortly afterward tweeting the name and photo of a man it said owes $170,000 in child support.
A spokeswoman with the DES told CNN that the department plans to "highlight" a total of 421 non-custodial parents who owe large amounts in child support accrued over the past five years.
"It’s simple. If you’re old enough to father a child, then you’re old enough to accept financial responsibility for that child," Ducey said in his address on Monday.
"If you don’t want your embarrassing, unlawful and irresponsible behavior going viral: Man up, and pay up," he added.