For those with healthy kidneys: No. For those with impaired kidney function, it is highly unlikely but one should still check with their medical doctor.
Please see our Creatine rubric for human clinical studies on the kidney. The net result was that even with one kidney, creatine had no negative effect on the kidneys. This is a topic that has been replicated numerous times in different populations by different researchers, and yet not a single peer-reviewed study or case report has surfaced where creatine is the causative factor behind kidney damage.
There is some confusion regarding the kidneys with the metabolite (waste product) of creatine, called 'creatinine', which is also a diagnostic criteria for kidney problems. This is a case of a supplement giving a 'false positive' and is in no way harmful, and can be read up more on our creatine disambiguation section.