In the local Universe, globular clusters (GCs) with metallicities $[{rm Fe}/{rm H}]<-2.5$ are extremely rare. In this Letter, the close connection between GC formation and galaxy evolution is used to show that this GC metallicity `floor results from the galaxy mass-metallicity relation of ultra low-luminosity galaxies (ULLGs) at high redshift, where the most metal-poor GCs must have formed. Galaxies with metallicities $[{rm Fe}/{rm H}]lesssim-2.5$ have too low masses to form GCs with initial masses $M_{rm i}gtrsim10^5~{rm M}_odot$, needed to survive for a Hubble time. This translates the galaxy mass-metallicity relation into a maximum initial cluster mass-metallicity relation for $[{rm Fe}/{rm H}]lesssim-1.8$, which naturally leads to the observed colour-magnitude relation of metal-poor GCs at $z=0$ (the `blue tilt). Its strength traces the slope of the gas phase mass-metallicity relation of ULLGs. Based on the observed blue tilt of GCs in the Virgo and Fornax Clusters, the galaxy mass-metallicity relation is predicted to have a slope of $alpha=0.4pm0.1$ for $10^5lesssim M_star/{rm M}_odotlesssim10^7$ at $zgtrsim2$. The GC metallicity floor implies a minimum host galaxy mass and a maximum redshift for GC formation. Any proto-GCs that may be detected at $z>9$ are most likely to end up in galaxies presently more massive than the Milky Way, whereas GCs in low-mass galaxies such as the Fornax dSph ($M_starapprox4times10^7~{rm M}_odot$) formed at $zlesssim3$.
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