We report the X-ray analysis of a sample of candidate high-redshift (1 < z < 2) Fanaroff–Riley type I (FR I) sources from the sample of Chiaberge et al., observed in the Chandra COSMOS field (C-COSMOS). Our main goals are to study their nuclear properties by means of unresolved X-ray emission, and to constrain the presence of clusters surrounding the FR I sources from the diffuse X-ray emission by the associated hot plasma. Among 19 FR I candidates, six have an X-ray-unresolved counterpart in the C-COSMOS catalogue. Two additional sources are not present in the C-COSMOS catalogue but are clearly detected in the Chandra images. X-ray spectral analysis, when possible, or hardness ratio of the stacked emission from X-ray-detected sources, suggests that some of them have significant intrinsic absorption (NH≳ 1022 cm−2), and high X-ray luminosities with respect to local FR Is. From the stacking analysis of the 11 non-detected sources, however, we find evidence for unresolved soft X-ray emission and no detected hard emission, suggesting an unabsorbed spectrum. Therefore, the X-ray properties vary significantly from source to source among these FR I candidates. From the analysis of the stacked images of all 19 FR I candidates we can rule out the presence of virialized haloes with temperatures larger than 2–3 keV; however, the upper limit on the average extended emission is still consistent with the presence of ∼1–2 keV hot gas.