East Africa is a high-risk area for malaria, both in the cities and remote areas. The good news is that Kilimanjaro is too cold at altitude for the mosquito which carries malaria, and it rarely ventures above 1200 metres. Of course, during your time in Tanzania, you will spend time at lower altitudes while on your way to and from your climb. You may even be combining the climb with a safari or some downtime in Zanzibar.
Those are the times when you are at risk. There is no vaccination against malaria, and the best way to protect yourself is to not get bitten in the first place. Wear long-sleeved shirts, long trousers and hats, use mosquito nets when sleeping and use insect repellent with 30% DEET, especially in the evenings when the malaria-carrying mosquito is active.
Your doctor will be able to advise on a suitable course of anti-malarial drugs courses, which must be started well before you travel – so consult in good time! The course involves taking tablets regularly, it must be completed and will continue for some time after you return home. Common drugs that may be prescribed include atovaquone/proguanil, doxycycline, mefloquine or primaquine.