A device for shutting off a pipe, the pipe allowing fluidic circulation of at least one fluid, the shut-off device having an in-line shut-off means for shutting off the pipe in a sealed manner and, conversely, for opening the pipe, an upstream valve arranged upstream of the in-line shut-off means, and a downstream valve arranged downstream of the in-line shut-off means. The shut-off device has an interlocking system for interlocking a member for tightly closing the in-line shut-off means with, for the one part, an upstream control member of the upstream valve and, for the other part, a downstream control member of the downstream valve, the interlocking system being movable in translation in a direction OX between a first end position and a second end position, the interlocking system having at least three separate parts assembled together.