Melamine is one of the most frequently detected adulterants in dairy products. The current study proposes a surface-enhanced Raman spectroscopy (SERS)-based analytical tool for fast and reliable screening of melamine in bovine milk. A hand-held Raman spectrometer was used in conjunction with a substrate composed of silver nanoparticles (AgNPs) that was 2D printed onto glass fiber (GF) filter paper. Under optimized conditions, a sensitive and fingerprint-like signal at 674 cm−1 was obtained. The AgNPs/GF substrate exhibited high sensitivity to melamine in milk down to 1.949 8 × 10−5 mg/mL, which is well below the USA and EU safety limits (2.5 × 10−3 mg/mL). Remarkably, the proposed technology was also highly reproducible, showing spot-to-spot and block-to-block variations below 3.3% and 4.9% at 674 cm−1 in Raman intensity, respectively. The characteristic peak intensity and concentration of melamine showed an acceptable linear relationship (R2 = 0.990 9) within the range of 0.000 1–1 mg/mL. Overall, the method established in this study can provide an efficient and effective method for the quantitative target screening and detection of melamine in dairy products.