It is almost certainly from the mains power. Even if your power supply is switching at a high frequency you can still pick up interference on the probes or sensor or other circuitry. Get a long electrical lead and go outside and see if the problem persists. – geometrikal
what @geometrikal said. Even if you have a really good power supply, some -60dB of what happens on the grid side will leak to your internal supply power. Now, guessing from your diagram ($f_\text{max} \approx 2\,\text{kHz}$, $\Delta_f = 2\,\text{Hz}$) I'd say I'm looking at a signal sampled at 4kHz, which has been subjected to a 2048-point FFT, abs(), semilogx plot.
So the plot contains half a second of information, and yet your highest peak is around $10^{-9}$. (By the way, I'm assuming that the base of this plot are processed samples, which don't directly represent the full ADC span as $[-1;+1]$. If it is, you should probably use an amplifier -- I don't think you have a ADC with a dynamic voltage range of 220dB -- that would be unusual.)
So, especially if the observed phenomena might be shorter than half a second, the relative strength of the power line harmonics might simply be caused by them being there throughout the whole measurement. This all comes down to you explaining (and maybe understanding) the nature of the signals you're visualizing. As a side note, I'd say the plot doesn't do a very good job at that -- you can barely see how the power in the highest frequencies seems to be higher than in the rest of the spectrum, and all I can say from this plot is "over the 100Hz to 2kHz range, power varies", which is not really much information.