By implementing the quantum renormalization group method, the effective Hamiltonian of the spin-12 Ising model with regularly altering strengths of both the magnetic fields and the exchange couplings are first derived analytically. Then, tripartite quantum discord (QD) and entropic uncertainty (EU) of the Ising model and their quantum phase transitions are investigated. Moreover, the quantum critical points and correlation length exponents of the model are analyzed, and both the block–block EU and the site–site EU are discussed through numerical calculations. It is found that under the system size increasing, the first derivatives of both tripartite QD and block–block EU show nonanalytic and scaling behaviors near the critical point. Furthermore, the strong quantum correlations among multi-particles do not necessarily lead to the decrease of EU, as the site–site EU in the vicinity of the critical point increases due to competitions among quantum correlations. The findings may offer new insights into utilizing EU as an observable of the quantum phase transitions.