Using a Butterworth high-pass filter together with Fast Fourier transform
As the comments say: it really depends on your signals. If the energy in the "don't care" region is significantly larger than the energy at the frequency of interest, it's helpful to pre-filter it first. Otherwise you may see "spectral leakage" of the high energy components into your target area. 

On the downside: the pre-filter will affect the group delay the transient response of your overall system. 

This being said: if the filter is not too steep and the cutoff frequency not too close to your target frequencies, pre-filtering is generally a good idea. The pre-filtering is much cheaper than the FFT, so it have almost no impact on CPU or memory requirements.