The licence, issued by the Ministry of Environment and Tourism, permits the hunting of the elephants and other wild animals for "complimentary purposes", according to local media reports. The country is holding nationwide festivities on Wednesday to mark the anniversary.
The Botswana-based Elephant Protection Society said the decision could undermine conservation. Chairman Oaitse Nawa told the BBC that elephants needed greater protection, warning that slaughtering elephants for celebratory feasting could encourage poaching by creating the impression that killing elephants is acceptable when sanctioned by government.
"Elephants have lost their social structures because they are always being pushed from one place to another by gunshots," Nawa said.
Concerns have also been raised on social media about eating game meat amid an outbreak of foot-and-mouth disease, which has prompted authorities to impose measures to contain its spread.
Tshenatshe Monwela, an elder in Maun, a tourism town in north-western Botswana, told local media that his community should have received buffalo instead. He argued that elephants had particular cultural and ecological significance, and that Botswana's historic role in protecting its wildlife and livestock should have been recognised in the allocation of meat for the anniversary celebrations.
Botswana is home to the world's largest elephant population, with more than 130,000 elephants.