The distribution of ejecta in young supernova remnants offers a powerful observational probe of their explosions and progenitors. Here we present a 3D reconstruction of the ejecta in SNR 0540-69.3, which is an O-rich remnant with a pulsar wind nebula located in the LMC. We use observations from the Very Large Telescope (VLT)/MUSE to study H beta, [O iii] lambda lambda 4959, 5007, H alpha, [S ii] lambda lambda 6717, 6731, [Ar iii] lambda 7136, and [S iii] lambda 9069. This is complemented by 2D spectra from VLT/X-shooter, which also cover [O ii] lambda lambda 3726, 3729, and [Fe ii] lambda 12567. We identify three main emission components: (i) clumpy rings in the inner nebula (less than or similar to 1000 km s(-1)) with similar morphologies in all lines; (ii) faint extended [O iii] emission dominated by an irregular ring-like structure with radius similar to 1600 km s(-1) and inclination similar to 40 degrees, but with maximal velocities reaching similar to 3000 km s(-1); and (iii) a blob of H alpha and H beta located southeast of the pulsar at velocities similar to 1500-3500 km s(-1). We analyze the geometry using a clump-finding algorithm and use the clumps in the [O iii] ring to estimate an age of 1146 +/- 116 yr. The observations favor an interpretation of the [O iii] ring as ejecta, while the origin of the H-blob is more uncertain. An alternative explanation is that it is the blown-off envelope of a binary companion. From the detection of Balmer lines in the innermost ejecta we confirm that SNR 0540 was a Type II supernova and that hydrogen was mixed down to low velocities in the explosion.