Anderson, an honorary director of the animal rights group People for the Ethical Treatment of Animals (PETA), described the plight of young pachyderms currently caged in holding pens as "heart-breaking".
"I am writing you to urge you to do everything in your power to assist in the efforts to stop such profiteering at the expense of wildlife," Anderson said in her letter to Environment Minister Saviour Kasukuwere.
The planned sale of the baby elephants has drawn condemnation following the publication of leaked images of the animals in holding pens.
"I have been deeply upset by the heart-breaking news about the 80 or so baby elephants who were torn away from their families, many even witnessing their own family's gruesome slaughter," the former Baywatch star said.
Zimbabwe wildlife authorities last December announced plans to export at least 62 elephants, saying that the country could cope with 42,000 elephants but had a population of 80,000.
They say the export would fund the running of game parks while a portion of the money would be allocated to communities bordering game reserves.
The elephants' exact destination has not been disclosed, but they are likely to be used as show animals or as zoo attractions.
Exporting elephants is not illegal, and Zimbabwe officials say the trade is within CITES (Convention on International Trade in Endangered Species) regulations.
Last year at least 300 elephants died in Hwange national park after poachers poisoned the environs of their watering halls with cyanide.
Park authorities said lack of funds limited patrols by game rangers leaving animals at the mercy of poachers.
A conference of elephant experts in Botswana last month heard that African elephants could be extinct in the wild within a few decades due to poaching for ivory.
The Zimbabwe government was not immediately available to comment on Anderson's letter.