The wavefront of an injection-seeded soft x-ray laser beam generated by amplification of high-harmonic pulses in a λ=18.9 nm molybdenum plasma amplifier was measured by a Hartmann wavefront sensor with an accuracy of λ/32 root mean square (rms). A significant improvement in wavefront aberrations of 0.51±0.03λ rms to 0.23±0.01λ rms was observed as a function of plasma column length. The variation of wavefront characteristic as a function time delay between the injection of the seed and peak of soft x-ray amplifier pump was studied. The measurements were used to reconstruct the soft x-ray source and confirm its high peak brightness.