The photo, posted on Kylie Jenner's Instagram at the beginning of the month, shows Willow lying on a bed next to shirtless Moises, seven years her senior.
Earlier this month Jada, 42, defended the picture, explaining to photographers:
'Here's the deal. There was nothing sexual about that picture of that situation. You guys are projecting your trash onto it … and you're acting like covert paedophiles and that's not cool.'
However according to an American website, the LA department of Child and Family Services have now launched an investigation into the post.
A source told the website: 'Social workers will also be talking separately with Willow, and they also want to talk to the young man in the picture with her as well.
'This won’t just be one or two visits with the family, and it will likely be an open investigation for at least a month, out of an abundance of caution.'
According to the reports, Jada and 45-year-old Will are being 'extremely cooperative'.
The couple, who have been married for 15 years, previously revealed that they don't believe in punishing their children.
'The way that we deal with our kids is, they are responsible for their lives. Our concept is, as young as possible, give them as much control over their lives as possible and the concept of punishment, our experience has been - it has a little too much of a negative quality.
'You can do anything you want as long as you can explain to me why that was the right thing to do for your life.'
Do you think the photo was inappropriate and do you agree with their parenting style? Let us know in the comments box below.