The retail giant buys around £1m worth of goods, including vegetables, from Zimbabwe each year.
Tesco said that although the amount was insignificant in terms of global trade and influence, it had taken the "difficult decision" to stop sourcing products from the country as long as the political crisis persists there.
The international community has condemned the presidential election re-run in Zimbabwe, in which Robert Mugabe claimed victory as the only candidate after opposition leader Morgan Tsvangirai pulled out citing violence against his supporters, many of whom have been murdered and beaten.
In a statement, Tesco said: "We cannot ignore the escalating political crisis in Zimbabwe, and the growing consensus in the international community -- including from UK politicians on all sides -- that further action must be taken to maximise the pressure for change."
The supermarket chain added that it was urgently looking for ways to support Zimbabwean workers who supplied Tesco, by other means.
The move to cut trade ties is a U-turn for Tesco, which said last week that it would be "irresponsible" to cut support to small farmers under the current conditions.
Peter Hain, the former Labour cabinet minister who called on supermarkets to end its trade with Zimbabwe, said: "This is a very welcome decision by Tesco. I hope it will give a lead to other British and global companies to freeze or suspend ties with Zimbabwe under Mugabe's tyranny."