Ornamental plant species introduced into new environments can exhibit an invasive potential and adaptability to abiotic stress factors. In this study, the drought stress responses of four potentially invasive ornamental grass species (Cymbopogon citratus, Cortaderia selloana, Pennisetum alopecuroides and P. setaceum) were analysed. Several seed germination parameters were determined under increasing polyethylene glycol (PEG 6000) concentrations. Additionally, plants in the vegetative stage were subjected to intermediate and severe water stress treatments for four weeks. All species registered high germination rates in control conditions (no stress treatment), even at high PEG concentrations, except C. citratus, which did not germinate at −1 MPa osmotic potential. Upon applying the water stress treatments, P. alopecuroides plants showed the highest tolerance, and C. citratus appeared the most susceptible to drought. Stress-induced changes in several biochemical markers (photosynthetic pigments, osmolytes, antioxidant compounds, root and shoot Na+ and K+ contents), highlighted different responses depending on the species and the stress treatments. Basically, drought tolerance seems to depend to a large extent on the active transport of Na+ and K+ cations to the aerial part of the plants, contributing to osmotic adjustment in all four species and, in the case of the most tolerant P. alopecuroides, on the increasing root K+ concentration under water deficit conditions. The study shows the invasive potential of all species, except C. citratus, in dry areas such as the Mediterranean region, especially in the current climate change scenario. Particular attention should be given to P. alopecuroides, which is widely commercialised in Europe as ornamental.