Due to their low mass and luminosity, M dwarfs are ideal targets if one hopes to find low-mass planets similar to Earth by using the radial velocity (RV) method. However, stellar magnetic cycles could add noise or even mimic the RV signal of a long-period companion. Following our previous work that studied the correlation between activity cycles and long-term RV variations for K dwarfs we now expand that research to the lower-end of the main sequence. Our objective is to detect any correlations between long-term activity variations and the observed RV of a sample of M dwarfs. We used a sample of 27 M-dwarfs with a median observational timespan of 5.9 years. The cross-correlation function (CCF) with its parameters RV, bisector inverse slope (BIS), full-width-at-half- maximum (FWHM) and contrast have been computed from the HARPS spectrum. The activity index have been derived using the Na I D doublet. These parameters were compared with the activity level of the stars to search for correlations. We detected RV variations up to ~5m/s that we can attribute to activity cycle effects. However, only 36% of the stars with long-term activity variability appear to have their RV affected by magnetic cycles, on the typical timescale of ~6 years. Therefore, we suggest a careful analysis of activity data when searching for extrasolar planets using long-timespan RV data.