A search for long-lived particles (LLPs) produced in association with a Z boson is presented. The study is performed using data from proton-proton collisions with a center-of-mass energy of 13 TeV recorded by the CMS experiment during 2016–2018, corresponding to an integrated luminosity of 117 fb−1. The LLPs are assumed to decay to a pair of standard model quarks that are identified as displaced jets within the CMS tracker system. Triggers and selections based on Z boson decays to electron or muon pairs improve the sensitivity to light LLPs (down to 15 GeV). This search provides sensitivity to beyond the standard model scenarios which predict LLPs produced in association with a Z boson. In particular, the results are interpreted in the context of exotic decays of the Higgs boson to a pair of scalar LLPs (H → SS). The Higgs boson decay branching fraction is constrained to values less than 6% for proper decay lengths of 10–100 mm and for LLP masses between 40 and 55 GeV. In the case of low-mass (≈ 15 GeV) scalar particles that subsequently decay to a pair of b quarks, the search is sensitive to branching fractions B(H → SS) < 20% for proper decay lengths of 10–50 mm. The use of associated production with a Z boson increases the sensitivity to low-mass LLPs of this analysis with respect to gluon fusion searches. In the case of 15 GeV scalar LLPs, the improvement corresponds to a factor of 2 at a proper decay length of 30 mm.