Results are reported from a search for the anomalous production of highly boosted Z bosons with large transverse momentum and decaying to dimuons. Such Z bosons may be produced in the decays of new heavy particles. The search uses pp collision data at sqrt(s) = 7 TeV, corresponding to an integrated luminosity of 5.0 inverse femtobarns recorded with the CMS detector. The shape of the observed transverse-momentum distribution of Z bosons is consistent with standard model expectations. Constraints are obtained on models predicting the production of excited quarks decaying via electroweak processes. Assuming a compositeness scale that is equal to the excited quark mass as well as transition coupling strengths between Z bosons and excited quarks that are equal to standard model couplings to quarks, masses of excited quarks below 1.94 TeV are excluded at the 95% confidence level. For excited quark production via a novel contact interactions, masses below 2.22 TeV are excluded, even if the excited quarks do not couple to gluons.