Therapeutic guava (Psidium guajava) leaf was used to green synthesize novel red-fluorescent graphene quantum dots (G-GQD) and their fluorescence quenching characteristic was exploited for the sensitive and selective detection of Hg(II), a hazardous metal pollutant, in aqueous media. An eco-friendly and low-cost approach was demonstrated for the preparation of fluorescent G-GQD by the one-pot single-step solvothermal treatment of guava leaf extracts, emitting in the far-red spectral region of 620 to 780 nm with the maximum intensity near 673 nm. The as-fabricated G-GQD revealed excitation wavelength (300–420 nm)-dependent as well as pH (2–7.2)-dependent fluorescence intensity, but without any shift in emission peak wavelength. The emission property of the as-fabricated G-GQD was utilized as a fluorescence turn-off probe for the selective quantification of aqueous Hg²⁺, with a limit of detection of 82 μM, over a large dynamic range of up to 0.38 mM. The effect of other co-existing metal salts, particularly the presence of paramagnetic ions, such as Cu²⁺, Co²⁺, Fe²⁺, and Al³⁺, which are known fluorescence quenchers, did not show any interference with Hg⁺² selectivity by the fluorescent G-GQD. These results indicate the potential applicability of the convenient, eco-friendly and cost-effective G-GQD for its rapid, selective, and sensitive fluorescence sensing response toward Hg(II) ion in polluted water bodies. Moreover, such a type of fabricated far-red emitting G-GQD not only overcomes the limitation of conventionally reported fluorescent GQD sensors emitting in the blue and green spectral regions, but also widens the horizon for different green-synthesized GQDs in metal and biochemical sensing applications also in the biologically advantageous red region of the visible spectrum.