We study the second-order weak correction to the muon anomalous magnetic moment in alternative electroweak gauge theories. The gauge-boson contributions are constrained by low-energy weak-interaction phenomenology. We examine the Higgs-boson contributions in three classes of models and find that they are potentially the dominant effect. Contributions of lepton-number-violating Higgs-boson interactions are calculated and included in the analysis. Severe limits on the spontaneous-symmetry-breaking scales and Yukawa couplings are found in some scenarios which have a separate scale for fermion masses, including the standard model with more than one doublet and a left-right model which naturally explains small neutrino masses. Higgs-boson effects may be detectable when order-of-magnitude improvements are made in the measurement of the muon anomalous magnetic moment.