The charity is calling on Associated British Foods (ABF) - as well as Coca-Cola and PepsiCo - to tighten supply chains to ensure the ingredients used in their products "are not grown on land that has been grabbed from communities that depend on it for their survival".
Oxfam's report, Nothing Sweet About It: How Sugar Fuels Land Grabs, claims that people are at risk of losing their homes and land in a rush to feed a growing appetite for sugar.
It links disputes over land with companies which supply sugar for Coca-Cola and PepsiCo products and also highlights alleged disputes with ABF, whose portfolio includes Silver Spoon, Twinings and Ovaltine.
Oxfam said it was campaigning against ABF on the basis that it is the second largest sugar producer in the world and the owner of the largest sugar producer in Africa, yet it "does not have policies to protect against land grabs".
It said there were also a number of reports linking the company to ongoing land disputes in its supply chain.
Sugar production is predicted to increase by 25% by 2020, with the global sugar trade already worth around £29 billion.
According to Oxfam, the world produced 176 million tonnes of sugar last year and the food and drinks industry accounted for more than half of it.
The charity said it had "largely gone unnoticed" that the sugar trade was "fuelling the problem of land grabs and disputes".
Oxfam's Behind The Brands campaign claims the world's 10 biggest food and drink companies lack strong enough policies to stop land grabs and disputes from featuring in their supply chains.
Oxfam chief executive Mark Goldring said: "We all need reassurance that what we are consuming is not contributing to the world's most vulnerable being evicted from their land without consent or compensation.
"Large corporations must take responsibility to ensure that their goods are not tainted by this scandal happening in remote places many miles from the board room.
"Associated British Foods, Coca-Cola and PepsiCo are among the world's biggest producers and buyers of sugar. They are in a prime position to stamp out land grabs by ensuring that the sugar they use is not grown on land that is taken against the wishes of the community. Their focus on this could transform the industry."
ABF said it was "unclear" as to why it had been included in Oxfam's report "given there is no evidence at all" of any "land grabs" on its behalf.
The company said in a statement: "ABF, through its African subsidiary Illovo, is and always has been hugely sensitive to issues of land ownership."
It cited examples of distributing company-owned cane land to black farmers and creating partnerships with local communities.
ABF said: "These are not the actions of a company which plays fast and loose with other people's land.
"Oxfam criticises ABF and Illovo for refusing to sign a pledge on land ownership. Pledges are cheap and plentiful. The history of Africa is full of them. The true test of any organisation is what it actually does. ABF and Illovo prefer to act on their beliefs and standards rather than pontificate about them.
"Illovo is a magnificent example of a company that works to the highest ethical standards to benefit the communities in which it operates."
A Coca-Cola spokeswoman said: "Through our sustainable agriculture guiding principles, we are asking our suppliers to recognise and safeguard the rights of communities to maintain access to land and natural resources.
"We are working to promote respect for human and workplace rights by the farm and the employer of workers at the farm, whether or not the employer is the farm itself."