Masche, 32, was taken into custody Sept. 11 at the Yavapi County Detention Center and released on $3,500 bond, a spokesman for Arizona's Camp Verde Marshal's Office tells PEOPLE.
The spokesman would not elaborate but confirmed published reports that Masche lost his temper, causing someone present to call 911. It is not known whether Masche's wife and TV costar, Jenny, was involved in the incident.
Masche is the father of Arizona's second-only set of sextuplets, born three years ago. The family currently lives in Florida.
According to the Camp Verde Bugle newspaper, Masche was arrested after allegedly threatening his family and beginning to yell and use profanities. When deputies arrived at the scene, Masche reportedly did not comply with authorities.
Had 'Total Brutal Fights'In an 2009 interview with PEOPLE, Bryan and Jenny admitted that raising six young children was not easy and that the couple argued. "We have totally brutal fights," Jenny told PEOPLE.
Relying upon their faith, the religious couple sought to work through their marital problems. "When you understand that there's no way out of marriage, that forces you to work on your marriage," Bryan told PEOPLE.
"We both have an understanding in our minds that there is no out," he added. "I know personally that I’m accountable to God, and Jenny knows she's accountable to God, and we don't have any way out of this thing. So if we’re going to be stuck with each other for the next 80 years, we better make it good."
Their marriage, said Jenny, "is a work in progress, and it's totally not perfect. But we believe that the stronger the couple is, the stronger the marriage is and the better it is for the children."
With additional reporting by LESLEY MESSER