A report posted on the CNN website said the broadcaster had not been given a reason for the ban by officials from the country's Ministry of Information and Publicity.
CNN said a ministry official, who did not want to be named, would also not reveal whether any international media organisations had been given permission to cover the election.
A network spokesperson said: "CNN regrets the Zimbabwean government's decision to deny us permission to enter the country to cover the parliamentary and presidential elections on Saturday March 29th.
"We hope that the government will reconsider its decision. CNN will continue to cover the elections as widely as possible from South Africa and surrounding countries."
South Africa's independent station e.tv and British TV networks ITV and Sky all said they were denied permission to cover the election as well.
The state-run Sunday Mail newspaper reported recently that at least 300 foreign journalists had applied for accreditation, but priority was being given to journalists from Africa and other developing nations that are sending election monitors.
The Mail reported: “There are unprecedented requests for field studios and most of the media organisations want to deploy their star anchorpersons. The CNN wants to deploy Nic Robertson, who is coming straight from Baghdad, while ITN wants to deploy the world renowned Jon Snow.”
The paper also quoted presidential spokesman George Charamba as saying: “The deployment of think-tanks suggests that the elections will be much more than a news item, while there is a strange alliance building between traditionally rival networks for the purposes of covering the elections.
"What this suggests is a shared objective. The story from Zimbabwe has to be uniformly echoed for propaganda purposes. Commercial rivalry has been set aside."
President Mugabe has barred Western observers from the 29 March elections in which he faces the challenge of his former finance minister, Simba Makoni, and opposition leader, Morgan Tsvangirai.
Article published courtesy of NewZimbabwe.com
