The eight dead rhinos were among 11 that were moved last month to Tsavo East National Park, where wildlife officials hoped they would start a new population.
The ministry said preliminary investigations had pointed to salt poisoning as the suspected cause of death.
The surviving translocated rhinos are also "being provided with fresh water in temporary water pans as we await the full postmortem examination report and further forensic investigations", the ministry said.
Save the Rhinos estimates there are fewer than 5,500 black rhinos in the world, all of them in Africa, while Kenya's black rhino population stands at 750, according to the Worldwide Fund for Nature.
Ms Kahumbu said the translocation could only be described as a complete disaster and sought reassurances that best practices in wildlife translocation would be adopted in future to prevent more deaths.
The number of African black rhinos dropped almost 98 percent from 1960 to 1995 before conservation efforts began to slowly rebuild the population.
"Moving rhinos is complicated, akin to moving gold bullion, it requires extremely careful planning and security due to the value of these rare animals", Kahumbu said in a statement. "We need to know what went wrong so that it never happens again".
Moreover, the last three of the 14 rhinos on the relocation list will no longer be moved to the park, the ministry noted. Park management is now closely monitoring the remaining three rhinos.
An global conservation group suspects that staff negligence may be a factor behind the latest deaths.
"Trans-locating wild animals of this size is a complex, challenging undertaking and not without risk. However, range expansion projects to increase black rhinos numbers are a recognised cornerstone of conservation efforts meaning translocations are crucial for future generations".
The black rhino deaths were "unprecedented" in over a decade of relocation efforts by the Kenyan Wildlife Service to save the vanishing species, said officials. It is unclear whether this rhino, taken from Nairobi National Park, was one of the eight who died in Tsavo East National Park.