Zebrafish Müller glia (MG) respond to retinal injury by suppressing Notch signaling and producing progenitors for retinal repair. A certain threshold of injury-derived signal must be exceeded in order to engage MG in a regenerative response (MG's injury-response threshold). Pan-retinal Notch inhibition expands the zone of injury-responsive MG at the site of focal injury, suggesting that Notch signaling regulates MG's injury-response threshold. We found that Notch signaling enhanced chromatin accessibility and gene expression at a subset of regeneration-associated genes in the uninjured retina. Two Notch effector genes, hey1 and id2b, were identified that reflect bifurcation of the Notch signaling pathway, and differentially regulate MG's injury-response threshold and proliferation of MG-derived progenitors. Furthermore, Notch signaling component gene repression in the injured retina suggests a role for Dll4, Dlb, and Notch3 in regulating Notch signaling in MG and epistasis experiments confirm that the Dll4/Dlb-Notch3-Hey1/Id2b signaling pathway regulates MG's injury-response threshold and proliferation.