Using CFHT-sis Fabry-Perot interferograms of the Wolf-Rayet ring nebula M1-67, we present an investigation of the statistical properties of fluctuating gas motions using structure functions (SFs) traced by Hα emission-line centroid velocities. We consider the SFs 〈|Δv(r)|p〉 of order p, i.e., the spatially averaged moments of order p of the spatial velocity increments at projected spatial scale r of M1-67's velocity field: we test for (i) SF scaling, 〈|Δv(r)|p〉 ∝ rζ(p), and (ii) nonlinearity of the observed scaling exponents ζ(p)s, as expected for intermittent flows. We find that there is a clear correlation at scales 0.02-0.22 pc between the mean quadratic differences of radial velocities and distance over the surface of M1-67. The first and second order SFs are found to scale as 〈|Δv(r)|〉 ∝ r0.5 and 〈|Δv(r)|2〉 ∝ r0.9 (Grosdidier et al. 2001). The former scaling law strongly suggests that supersonic turbulence is at play in M1-67, on the other hand, the latter scaling law agrees very well with Larson-type laws for velocity turbulence. Additionally, we can discuss the nature of the turbulence in terms of Universal Multifractals (UM), a continuous-scale limit of multiplicative cascades (Schertzer & Lovejoy 1987) and derive the level of intermittency in the nebula.