Recently, we have shown that the physiological roles of a multifunctional protein fructose 1,6-bisphosphatase 2 (FBP2, also called muscle FBP) depend on the oligomeric state of the protein. Here, we present several lines of evidence that in HL-1 cardiomyocytes, a forced, chemically induced reduction in the FBP2 dimer-tetramer ratio that imitates AMP and NAD+ action and restricts FBP2-mitochondria interaction, results in an increase in Tau phosphorylation, augmentation of FBP2-Tau and FBP2-MAP1B interactions, disturbance of tubulin network, marked reduction in the speed of mitochondrial trafficking and increase in mitophagy. These results not only highlight the significance of oligomerization for the regulation of FBP2 physiological role in the cell, but they also demonstrate a novel, important cellular function of this multitasking protein—a function that might be crucial for processes that take place during physiological and pathological cardiac remodeling, and during the onset of diseases which are rooted in the destabilization of MT and/or mitochondrial network dynamics.