Craig said police in the Detroit area were aware of the video's circulation, but initially were "unaware that the actual suspect" had a connection to Detroit.
Germaine Moore, 44, is now being held at Elmore County Jail.
The Wayne County Prosecutor's Office says the assaults happened while Moore was babysitting the kids while their mother was at work.
Alabama law enforcement officers last week announced the investigation, and also warned about distributing the video. Those charges include sexual assault of a child, distribution of a video of the assault and first-degree criminal sexual conduct, police said.
Officers across the country are issuing a warning after the arrest of a man wanted for a child porn video that's been shared around the world.
The victim in the video has been located and is safe.
Police did make another arrest for distribution of the video - 42-year-old Jerrell Washington.
YouTube Go, the company's offline viewing app, expands to 130 countries
Some design changes have also been made to make it easier for you to access the "Share Nearby" feature right from the homepage. The expansion comes after more than a year of beta availability in India and 14 other Asian and African nations.
Wayne County Prosecutor Kym Worthy's office is arranging to have Moore extradited to MI from his Alabama home.
Kansas City Police told one of FOX4's reporters that they had received many complaints and concerns about the video after individuals in the community had received it via social media.
Raleigh police told city residents that possession, dissemination or sharing of the video or similar videos is a criminal act: second-degree sexual exploitation of a minor.
Moore is the children's relative. In addition to the Alabama charges, Moore faces active warrants in Detroit, Alabama authorities reported.
Washington was taken into custody late Monday afternoon by the U.S. Marshals Fugitive Task Force.
Investigators say the video in question made it all the way to France. He is being held on a $100,000 bond at the Montgomery County Detention Facility. "Do not share it, as criminal charges may result".
He was charged in Detroit with molesting three children, ages 9, 10 and 12, while they were being babysat at his mother's Detroit home. "We, just like you, want the person (s) that are abusing this child captured and brought to justice". Regardless of intention, sharing such imagery is harmful and illegal. "We urge people never to share such content and to report it to local authorities immediately".