In this work, yellow emissive carbon dots (Y-CDs) were prepared via a simple hydrothermal method using catechol and hydrazine hydrate as the carbon and nitrogen sources, respectively. The average particle size was 2.99 nm. The Y-CDs demonstrate excitation-dependent emission properties, and the maximum emission wavelength is 570 nm at E_x = 420 nm. The fluorescence quantum yield is calculated to be 28.2%. Ag⁺ could quench the fluorescence of Y-CDs with high selectivity. The quenching mechanism was further explored by various characterization techniques. A sensitive fluorescent probe for Ag⁺ detection was established based on Y-CDs with a linear range of 3–300 μM. The detection limit was calculated to be 1.1 μM. The proposed method shows satisfactory results in real water samples without interference by coexistence.