Leishmaniosis (or leishmaniasis) is a neglected parasitosis most commonly transmitted by the sandfly bite. Changes in temperature, precipitation, and humidity can greatly affect the vectors and reservoir hosts. This study aimed to determine the association between temperature, air humidity, and weather conditions with the incidence of leishmaniasis in Montenegro during a seven-decade period (1945–2014) and to statistically compare and correlate the obtained data. In the studied period, there were 165 registered cases of leishmaniosis, 96.4%, in the coastal and central region of Montenegro, with an average incidence rate of 0.45/100.000. The visceral form of leishmaniosis predominated (99% of the cases), with only one case of cutaneous disease. Climate factors (average temperature, air humidity, and precipitation) had an impact on the occurrence of leishmaniosis in Montenegro. Air temperature elevated by 1 °C in all regions of Montenegro was significantly correlated with an increased incidence of leishmaniosis, by 0.150 (0.013 to 0.287; p < 0.05). In order to improve prevention and control of this disease, it is also necessary to investigate other factors with a possible impact on the number of cases of this neglected parasitosis.