The photo in question finds Willow laying in bed with Moises Arias, 20, as he sits shirtless with his back to a wall.
According to Radar Online, the Los Angeles Department of Children and Family Services opened an investigation last week after the image went viral online and was deemed inappropriate by several media outlets.
"Will and Jada Pinkett Smith have been extremely cooperative with officials. Of course, they aren't happy that their parenting skills are under scrutiny, but they understand," a source told Radar.
The insider added that social workers also plan to meet with Willow and Arias separately, and that the investigation is expected to last least one month "out of abundance of caution."
A day after the picture made headlines Pinkett Smith told photographers that "there was nothing sexual about that picture or that situation."
"You guys are projecting your trash onto it," she said at the time. "You're acting like covert pedophiles and that's not cool."
Arias is best known for playing the role of Rico in Disney's Hannah Montana from 2006 to 2011.