Abstract In wetlands, hydrochory is one of the main mechanisms of seed dispersal and there is often synchrony between propagule production and the flood season. Different sources of disturbance can prevent seed dispersal to suitable sites, and if environmental conditions are not adequate for germination and seedling establishment, recruitment will be limited, affecting succession. We worked in a disturbed tropical freshwater swamp where the native grass Leersia hexandra has dominated open areas, creating a grass matrix that surrounds patches of swamp forest. Leersia grows vigorously, forming cushions of dry matter that cover the soil, forming a potential obstacle to seed dispersal. We asked whether the vegetative growth of this grass prevents the entry and dispersal of seeds of the tropical swamp tree Pachira aquatica, thwarting seed germination and seedling establishment, and arresting succession. We set up transects in the grass matrix in two zones: close to the river (R) and bordering the tree patches or fragments (F). We quantified tree seed and seedling presence, survival and growth in situ and experimentally introduced seeds and seedlings in the field and monitored seed germination and the survival and growth of their seedlings, as well as that of transplanted seedlings. There was a negative relationship between the number of seeds and established seedlings, and the distance to river or fragment (r = −0.86, p < 0.001 for zone R; and r = −0.77, p < 0.001 for zone F) and with the grass cushion (r = −0.68, p = 0.005 for zone R; and r = −0.66, p = 0.007 for zone F); the grass creating a barrier to dispersal. When seeds were sown after clearing the grass cushion, germination success was high, so this stage is not limited. The transplanted seedlings had better survival and a greater final height than the seedlings of the sown seeds. Grass cover had a negative effect on both types of seedlings. Seedling survival rates were inversely related to grass cover, showing that seedlings overgrown by grass had low survival rates. Flooding is a stress factor for seedlings and produced mortality, in addition to the effects of the grass. Together, the field survey and the experiment show that succession is being arrested in two ways: (1) by limiting seed dispersal because the grass cushion slows the dispersal and penetration of seeds into the vegetation; and (2) by limiting seedling establishment because the grass competes for space and light. Our results show that even where the grass is native, slower growing, seed‐dependent species may struggle to compete and establish. If grass cover is increasing, these swamps are very vulnerable to a decrease in area because it is very difficult for them to regenerate naturally.