In the footage, some Kenyan soldiers can be seen carrying white shopping bags, while others appear to take white boxes from a mobile phone store.
At least 67 people died when suspected al-Shabab militants stormed the Nairobi shopping centre on 21 September.
The Kenyan military says it is investigating the looting allegations.
The CCTV footage is taken inside the entrance to the Westgate mall's Nakumatt supermarket, which sells everything from food to televisions, News agencies say.
In one section of footage, several soldiers are seen walking out of the supermarket, past a blood-spattered floor, carrying large plastic carrier bags.
In another clip, Kenyan soldiers can be seen next to a mobile phone outlet. One reaches over the counter, and apparently removes a white item.
Then more soldiers remove white items, which the Reuters news agency describes as mobile phone boxes.
The Kenyan military says it has launched an investigation into the looting allegations, which reports say will have angered many Kenyans.
