Hypernovae powered by magnetic jets launched from the surface of rapidly rotating millisecond magnetars are one of the leading models to explain broad-lined Type Ic supernovae (SNe Ic-BL), and have been implicated as an important source of metal enrichment in the early Universe. We investigate the nucleosynthesis in such jet-driven hypernovae using a parametrized, but physically motivated, approach that analytically relates an artificially injected jet energy flux to the power available from the energy in differential rotation in the protoneutron star. We find ejected 56Ni masses of 0.05 -0.45M⊙ in our most energetic models with explosion energy > 1052 erg. This is in good agreement with the range of observationally inferred values for SNe Ic-BL. The 56Ni is mostly synthesized in the shocked stellar envelope, and is therefore only moderately sensitive to the jet composition. Jets with a high electron fraction Ye = 0.5 eject more 56Ni by a factor of 2 than neutron-rich jets. We can obtain chemical abundance profiles in good agreement with the average chemical signature observed in extremely metal-poor (EMP) stars presumably polluted by hypernova ejecta. Notably, [Zn/Fe] ≳ 0.5 is consistently produced in our models. For neutron-rich jets, there is a significant r-process component, and agreement with EMP star abundances in fact requires either a limited contribution from neutron-rich jets or a stronger dilution of r-process material in the interstellar medium than for the slow SN ejecta outside the jet. The high [C/Fe] ≳ 0.7 observed in many EMP stars cannot be consistently achieved due to the large mass of iron in the ejecta, however, and remains a challenge for jet-driven hypernovae based on the magnetorotational mechanism. © 2021 The Author(s).