A bstract We explore the extent to which future precision measurements of the Standard Model (SM) observables at the proposed Z -factories and Higgs factories may have impacts on new physics beyond the Standard Model, as illustrated by studying the Type-I Two-Higgs-doublet model (Type-I 2HDM). We include the contributions from the heavy Higgs bosons at the tree-level and at the one-loop level in a full model-parameter space. While only small tan β region is strongly constrained at tree level, the large tan β region gets constrained at loop level due to tan β enhanced tri-Higgs couplings. We perform a multiple variable χ 2 fit with non-alignment and non-degenerate masses. We find that the allowed parameter ranges could be tightly constrained by the future Higgs precision measurements, especially for small and large values of tan β . Indirect limits on the masses of heavy Higgs bosons can be obtained, which can be complementary to the direct searches of the heavy Higgs bosons at hadron colliders. We also find that the expected accuracies at the Z -pole and at a Higgs factory are quite complementary in constraining mass splittings of heavy Higgs bosons. The typical results are | cos( β − α ) | < 0 . 05 , | ∆ m Φ | < 200 GeV, and tan β ≳ 0 . 3. The reaches from CEPC, Fcc-ee and ILC are also compared, for both Higgs and Z -pole precision measurements. Comparing to the Type-II 2HDM, the 95% C.L. allowed range of cos( β − α ) is larger, especially for large values of tan β .