Self-assembled monolayers (SAMs) have been widely used to engineer the electronic properties of substrate-supported graphene devices. However, little is known about how the surface chemistry of SAMs affects the interfacial mechanical properties of graphene supported on SAMs. Fluctuations and changes in these properties affect the stress transfer between substrate and the supported graphene and thus the performance of graphene-based devices. The changes in interfacial mechanical properties can be characterized by measuring the out-of-plane elastic properties. Combining contact resonance atomic force microcopy experiments with molecular dynamics simulations, we show that the head group chemistry of a SAM, which affects the interfacial interactions, can have a significant effect on the out-of-plane elastic modulus of the graphene-SAM heterostructure. Graphene supported on hydrophobic SAMs leads to heterostructures stiffer than those of graphene supported on hydrophilic SAMs, which is largely due to fewer water molecules present at the graphene-SAM interface. Our results provide an important, and often overlooked, insight into the mechanical properties of substrate-supported graphene electronics.