The interplay between electron-electron and electron-phonon interactions is one of the central topics in condensed matter physics. Although the density functional theory plus Hubbard U correction method (DFT+U) is broadly used to study electronic structure of strongly correlated materials, the extension of this method to electron-phonon g matrix and electron-phonon coupling has received limited attention. In this work, we implement an algorithm that integrates DFT+U and frozen phonon method (also known as the finite-displacement method) for phonon and electron-phonon g matrix calculations. We obtain Hubbard U corrections not only applied on electronic and phonon band structures, but more importantly also on electron-phonon g matrix. We demonstrate our algorithm in two prototypical correlated materials: infinite-layer nickelates LaNiO2 and ruthenium dioxide RuO2. We find that i) while the Hubbard U corrections weakly increase the electron-phonon interaction of 20% hole-doped LaNiO2, its total electron-phonon coupling remains small and not sufficient enough to account for the observed superconducting transition temperature of about 10-30 K. Our results contrast with the recent work showing that the full GW corrections yield an elevated electron-phonon coupling of 20% hole-doped LaNiO2 five times larger than its DFT value. ii) The Hubbard U corrections remove the imaginary phonon modes of RuO2 when strained on TiO2 substrate and substantially reduce its electron-phonon coupling. Our results alleviate the discrepancy between the previously reported large theoretical electron-phonon coupling and the low superconducting transition temperature observed experimentally. Our work provides an algorithm that fully includes the Hubbard U corrections on electron-phonon properties of correlated materials, and highlights the importance of Fermi surface shape and correlation effects on phonon spectrum and electron-phonon g matrix.