Diagnosis is crucial to increase the success rate of cancer treatments as well as the survival rate and life quality of patients, in particular for forms of cancer that remain largely asymptomatic until metastasis. Methodologies that allow the diagnosis of early-stage tumors as well as the detection of residual disease have the potential to improve cancer control and help monitor therapeutic outcomes. In this work, we report a Laser-Induced Breakdown Spectroscopy (LIBS) approach to early diagnosis of a form of skin cancer, melanoma, based on the analysis of biological fluids (blood and tissue homogenates) harvested from diseased mice and healthy controls. We acquired femtosecond LIBS spectra and used two different approaches for the analysis: through comparison of the emission intensity of selected analytes in healthy and diseased samples; and by using machine learning classification algorithms (LDA, Linear Discriminant Analysis; FDA, Fisher Discriminant Analysis; SVM, Support Vector Machines; and Gradient Boosting). We also addressed the effect of substrates on the analysis of liquid samples, by using four different substrates (PVDF, Cu, Al, Si) and comparing their performance. We show that with a combination of the most appropriate substrate and algorithm, we are able to discriminate between healthy and diseased mice with accuracy up to 96% while direct analysis of LIBS spectra did not provide any conclusive results. These series of results demonstrate that carefully designed LIBS measurements combined with machine learning can be a powerful and practical approach for the diagnosis of cancer.