JOHANNESBURG—South Africa’s government on Thursday denounced a tweet by President Donald Trump in which he referred to “large scale killing of farmers” in the country, Africa’s most-developed economy.

Mr. Trump’s overnight tweet referenced a report by Fox News host Tucker Carlson attacking South African plans to redistribute more land from white to black citizens and suggesting that the U.S. government should take a more critical stance. In the tweet, Mr. Trump asked Secretary of State Mike Pompeo to study the issue.

The...