The apparatus according to the invention comprises a coupler (30) intended to couple between each other two monomode fibres presenting four branches (31, 32, 33, 34). The branch (31) is connected to a branch (36). The branch (33) is the reference fibre and forms with a converging optics (39) and a plane mirror (41) a delay line. The branch (32) is aligned at (37) with the fibre to be measured (38) associated to a mirror (42). The light reflected by the mirrors (41 and 42) forms interference fringes which are used to determine the chromatic dispersion of the fibre to be measured (38).