Two children and one adult in the Zambezi Valley have died of the disease, which also threatens to kill 60,000 livestock in the region, Save the Children, a British non-government group, said in a statement.
Anthrax is a highly contagious infection that usually only afflicts livestock, but can be transmitted to humans who handle or eat infected animals.
Rachel Pounds, Save the Children's country director in Zimbabwe, said devastating food shortages were leading families to eat meat even from animals they know have died of anthrax.
"Many families in the Zambezi Valley are so hungry that they are taking meat from the carcasses of their dead animals, even if they know it's diseased, and are feeding it to their children," she said.
"If the animal has been poisoned by anthrax, those children could die," she added, calling the outbreak the biggest in Zimbabwe in nearly three decades.
Authorities have imposed quarantines to prevent the disease from spreading, but Pounds said that Zimbabwe's economic collapse left the country with few means to enforce them.
Zimbabwe is battling a nationwide cholera epidemic that has killed 425 people since late August and infected more than 11,000, according to government statistics.
Zimbabwe has been reduced to abject poverty after a decade of economic crisis and President Robert Mugabe's heavy-handed response to a political challenge from the opposition Movement for Democratic Change.