The star of Black Swan was being interviewed along with Friends With Benefits co-star Justin Timberlake when she was shown the clip.
In it Sgt Scott Moore asked her to be his date for the Marine Corps Ball in November.
He is currently serving with 3rd Battalion 2nd Marines in Afghanistan.
In the video he introduces himself as Sergeant Moore but says she can call him Scotty.
Walking through a heavily-fortified compound with shaved head, glasses and in full combat gear he looked into a friend's video camera and addressed her directly.
"I just want to take a moment out of my day to invite you to the Marine Corps Ball on 18 November in Greenville, North Carolina, with yours truly," he said.
"So take a second, think about it and get back to me."
The 25-year-old actress was surprised at first but then asked for details.
That's when Justin Timberlake stepped in.
"Have you seen this? Have you heard about this? You need to do it for your country."
After being persuaded, Mila Kunis then looked into the camera and told Moore that she was going to make it happen.