Heart-rate variability has proved a valid tool in prognosis definition of patients with congestive heart failure (CHF). Previous research has documented Poincaré plot analysis as a valuable approach to study heart-rate variability performance among different subjects. In this paper, we explored the possibility to feed machine-learning (ML) algorithms using unconventional quantitative parameters extracted from Poincaré plots (generated from 24-h electrocardiogram recordings) to classify patients with CHF belonging to different New York Heart Association (NYHA) classes. We performed in sequence the following investigations: first, a statistical analysis was carried out on 9 morphological parameters, automatically measured from Poincaré plots. Subsequently, a feature selection through a wrapper with a 10-fold cross-validation method was performed to find the best subset of features which maximized the classification accuracy for each considered ML algorithm. Finally, patient classification was assessed through a ML analysis using AdaBoost of Decision Tree, k-Nearest Neighbors and Naive Bayes algorithms. A univariate statistical analysis proved 5 out of 9 parameters presented statistically significant differences among patients of distinct NYHA classes; similarly, a multivariate logistic regression confirmed the importance of the parameter ρy in the separability between low-risk and high-risk classes. The ML analysis achieved promising results in terms of evaluation metrics (especially the Naive Bayes algorithm), with accuracies greater than 80% and Area Under the Receiver Operating Curve indices greater than 0.7 for the overall three algorithms. The study indicates the proposed features have a predictive power to discriminate the NYHA classes, to which the features seem evenly correlated. Despite the NYHA classification being subjective and easily recognized by cardiologists, the potential relevance in the clinical cardiology of the proposed features and the promising ML results implies the methodology could be a valuable approach to automatically classify CHF. Future investigations on enriched datasets may further confirm the presented evidence.