The actress was wearing a black jumper while standing over a man during the clip which could be seen on Monday evening.
In what is believed to be an action movie, she then removed her bra to reveal her breasts during the striptease.
A television source told The Sun: "This has gone down like a lead balloon at the BBC. It is totally unprofessional.
"It beggars belief a sex scene should be played live on air. The employee is on borrowed time when bosses catch up with him."
Viewer Lyndsey Robinson noticed the man watching the clip and posted a video of it on her Facebook page and wrote: "Did anyone else notice news last night on BBC???
"Thought I was seeing things...but just re-wached On iplayer...nope I definitly saw what I thought I had (sic)."
The BBC said it is investigating the incident.
During their time at Broadcasting House in central London, BBC employees have been caught chatting, yawning, flirting and playfighting in the open-plan office.
In June, BBC News anchor Huw Edwards fell victim to a technical glitch on News at Ten and was seen twiddling his thumbs for two-and-a-half minutes.
He was unaware he was live on air and later tweeted a picture of a Welsh beer to celebrate getting through the shift.
On Monday, just hours before the striptease incident, newsreader Simon McCoy was heard sighing throughout his report on a dog surfing competition in California.
He continued to sigh his way through the report and his face fell in despondency when he said "here are the pictures."
