A fluid dispenser device comprising: a reservoir (10) containing fluid; a dispenser head (20) that is provided with a dispenser orifice (21); dispenser means (25) for dispensing at least a fraction of said fluid through said dispenser orifice (21); and passage means (40) for connecting said reservoir (10) to said dispenser orifice (21) on actuation of said dispenser means (25), said device further comprising at least one porous insert (50) that is made out of porous material so as to suck up, in particular by capillarity, and to trap, at least in part, any residual fluid after actuation; said reservoir (10) including a stopper (25) that closes said reservoir (10) in leaktight manner before actuation.