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.
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.
Heroes of attack
Victims of attack
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.
It is still not clear whether some of the attackers might have escaped.
The Somali militant group al-Shabab said its members staged the attack in response to Kenya's army carrying out operations on Somali territory.
Last week, the BBC's Newsnight programme revealed that one of the suspected attackers was believed to be a 23-year-old Somalia-born Norwegian national, Hassan Abdi Dhuhulow.
His family fled to Norway in the 1990s, but he returned to Somalia in 2009 and allegedly joined the Somali militant group.
Sources in al-Shabab have told the BBC Somali Service that Dhuhulow attended a training camp in El Bur in central Somalia, one of the militants' main bases.
The sources said Dhuhulow took part in many al-Shabab operations in Mogadishu and Kismayo and was well-known in jihadist circles.
Security camera footage has emerged which appears to show Kenyan security forces looting goods during last month's siege of the Westgate mall.