Building upon recent theoretical and experimental work on two-dimensional labyrinthine acoustic metamaterials, we design, fabricate, and characterize nearly isotropic three-dimensional airborne acoustic labyrinthine metamaterials. Our experiments on aluminum-based structures show phase and group velocities smaller than that of air by a factor of about 8 over a broad range of frequencies from 1 to 4 kHz. This behavior is in agreement with three-dimensional band-structure calculations including the first and higher bands. The extracted imaginary parts of the phase velocity are 5–25 times smaller than the mentioned real parts. This ratio is better than for most optical metamaterials but still rather favors applications in terms of sub-wavelength broadband acoustic absorbers.