The unnamed man was among a group of tourists staying at a non-designated camping site on the Huab river in the Kunene region of northwestern Namibia, the ministry said in a statement on its Facebook page.
“This is a very unfortunate incident and highly regrettable,” the statement said.
“We wish to express our sincere condolences to the bereaved family and friends of the deceased.”
No further details were provided about how the man died.
The ministry and police were investigating and hoped to establish whether the tour group had a guide, the statement said.
The Australia Department of Foreign Affairs and Trade told CNN it is seeking to confirm the report.
“We stand ready to offer consular assistance to any Australian citizen, should they request it,” a spokesperson said.
The ministry warned visitors to the country to “be cautious and adhere to the rules and regulations put in place for their safety.”