ABSTRACT Observations of the Faraday rotation measure, combined with the dispersion measure, can be used to infer the magnetoionic environment of a radio source. We investigate the magnetoionic environments of fast radio bursts (FRBs) by deriving their estimated average magnetic field strengths along the line of sight 〈B∥〉 in their host galaxies and comparing them with those of Galactic pulsars and magnetars. We find that for those FRBs with RM measurements, the mean 〈B∥〉 are $1.77^{+9.01}_{-1.48}\, \rm μ G$ and $1.74^{+14.82}_{-1.55}\, \rm μ G$ using two different methods, which is slightly larger but not inconsistent with the distribution of Galactic pulsars, $1.00^{+1.51}_{-0.60}\, \rm μ G$. Only six Galactic magnetars have estimated 〈B∥〉. Excluding PSR J1745–2900 that has an anomalously high value due to its proximity with the Galactic Centre, the other five sources have a mean value of $1.70\, \rm μ G$, which is statistically consistent with the 〈B∥〉 distributions of both Galactic pulsars and FRBs. There is no apparent trend of evolution of magnetar 〈B∥〉 as a function of age or surface magnetic field strength. Galactic pulsars and magnetars close to the Galactic Centre have relatively larger 〈B∥〉 values than other pulsars/magnetars. We discuss the implications of these results for the magnetoionic environments of FRB 121102 within the context of magnetar model and the model invoking a supermassive black hole, and for the origin of FRBs in general.