Will Smith and wife Jada Pinkett Smith are under investigation by child protective services over a photo of their 13-year-old daughter Willow lying on a bed with her friend, Moises Arias, 20, according to a report.

The controversial black and white snap, which was posted on social media, depicted actor Moises shirtless with Willow slouched fully clothed in front of him.

Willow's mother Jada, 42, defended the image earlier this month, saying there was 'nothing sexual about it'.

Now the Los Angeles Department of Children And Family Services has launched a probe, according to reports.

The website reports the investigation was launched last week and that Will, 45, and Jada have been 'extremely cooperative'.

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.'

Moises posted the picture earlier this month on social media. It was then noticed on their friend Kylie Jenner's Tumblr account, leading to a media furor.

When asked about the photo, Jada lashed out at photographers and videographers as she arrived at Los Angeles Internation Airport on May 7.