Soldiers from the two sides are in a stand-off in Doklam, an area between China and Indian ally Bhutan.
New Delhi sent soldiers in June to stop China from constructing a road there.
The Hindustan Times said the three-minute Xinhua video has "racist overtones" and "mocked and parodied Indians".
The video appears to be an attempt to use humour to win over foreign audiences.
It has been posted on Twitter and YouTube, both of which the ruling Communist Party tries to block Chinese internet users from seeing.
It accuses Indian forces of trespassing and breaking international law.
"Didn't your mama tell you, never break the law?" says the host, identified as Dier Wang.
The video includes appearances by a man in a turban, sunglasses and false beard who speaks in an exaggerated Indian accent over canned laughter.