In the footage, some 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 September 21.
The Kenyan military says it is investigating the looting allegations.
News agencies say the CCTV footage is taken inside the entrance to the Westgate mall’s Nakumatt supermarket, which sells everything from food to televisions.
In one section of footage, several soldiers are seen walking out of the supermarket, past a blood-spattered floor, carrying 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 Westgate attack sparked a four-day siege in which large parts of the shopping centre were destroyed.
The Kenyan military says it has launched an investigation into the looting allegations, which correspondents say will have angered many Kenyans.
At the weekend, Kenya’s biggest-selling newspaper, The Nation, ran an article entitled Shame of soldiers looting Westgate.
The footage of the alleged looting emerged as the Kenyan authorities announced they had recovered the body of what they consider to be a fourth attacker.
“Today, Sunday 20 October 2013, we recovered a fourth body, which we know from CCTV footage to be that of a terrorist,” said the Kenyan interior minister, Joseph Ole Lenku.
“DNA and other investigations will confirm their identities. We have also recovered four AK47 assault rifles which we know were used by the terrorists in the assault. We also recovered 11 magazines of AK47 assault rifles.”
Officials had initially said 10 to 15 gunmen were involved, but CCTV footage appears to show only four militants.
O8_Jhri2Y5sImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…