Reduced ejection fraction (EF), possibly induced/mediated by autonomic abnormal activation, is one of the most powerful predictors of adverse outcome after acute myocardial infarction (MI). A deep understanding of the correlation between the autonomous functionality and the left ventricular performance in these patients is therefore of paramount importance. The autonomous function is reflected in the cardiac activity and, specifically, in the heart rate variability (HRV) signal. Given the cardiac activity nonlinearity, growing interest is being manifested towards nonlinear methods of analysis, which might provide more significant information than the traditional linear approaches. The aim of the present study was to investigate if non-linear HRV metrics change between MI patients with preserved EF (pEF) and MI patients with reduced EF (rEF). Data were acquired in the context of the cardioRisk project. Ten MI patients with rEF and six MI patients with pEF, admitted to Intensive Cardiac Care after a first acute MI episode, were studied. The ECG was acquired during a Holter recording and the tachogram was extracted. Sample entropy (SE) and Lempel-Ziv Complexity (LZC 1 and LZC 2) metrics were computed on five hour long tachogram portions. A significant correlation was found between LZC indices and EF in the whole population; SE, LZC 1 and LZC 2 were significantly higher in patients with pEF. Our results indicate that lower complexity characterizes the HRV of MI patients with rEF. Complexity reduction might be due to a simplification of regulatory mechanisms, which might explain why MI patients with rEF are at higher risk for subsequent non-fatal and fatal events.