The internal ocean of Jupiter’s moon Europa is thought to be a prime candidate for hosting extraterrestrial life. Europa’s silicate interior may contribute to habitability via the generation of reactants through hydrothermal activity, serpentinization, or other geological processes occurring on or just below Europa’s seafloor. However, silicate melting is thought to occur at >100 km depth in Europa’s mantle and it is unknown if this magma is able to penetrate and travel through the moon’s likely thick, brittle lithosphere to erupt at the seafloor. Here we combine previous modeling approaches to Europan interior melt generation and lithospheric dyke transport to show that Europan seafloor volcanism is strongly inhibited by its lithosphere. The low stress state of the Europan interior hinders the ability of dykes to penetrate through the lithosphere. Should dykes form, they penetrate <5% of the 200–250 km-thick lithosphere. Low mantle melt fractions (3–5%) drive sluggish pore-space magma flow, leading to dyke influxes 10,000 times lower than that necessary for seafloor eruption. These results strongly suggest that models of Europan habitability reliant on present-day volcanism at its seafloor are implausible.