We report a thorough analysis of the spectral properties of an ytterbium-doped fibre amplifier, seeded by a Nd:YAG laser, whose linewidth has been narrowed down to 1 Hz by locking the laser to an ultrastable reference cavity. We measured the phase noise contribution from the amplifier, showing that it does not depend on the amplification gain, nor on the seed laser linewidth. Moreover, the amplifier-induced phase noise does not affect the final linewidth, as verified by heterodyne linewidth measurement within the 0.2 Hz resolution bandwidth of our acquisition set-up. Preservation of spectral purity below Hz-level is promising for more demanding applications, from nonlinear optics to frequency/time-standard transfer over fibre links.