Minimum sampling frequency for any signal should be at least twice the frequency of the highest frequency component in your signal as it is stated in the Nyquist sampling theorem. 

Please look at these links (I think that the first one is easy to read):

Usually, EEG is filtered with a low pass filter with a cutoff frequency of  50Hz. So in theory, after filtration, all the components of the signal should have frequencies that are lower than 50Hz. So the minimum sample rate should be twice the 50Hz so it should be at least 100Hz.

Please note that that is the theoretical minimum that you need to satisfy. In order to have a more practical solution and nice-looking signal, usually, people sample EEG signal with few hundreds of Hz. Typically around 300Hz.