We adapt the smooth tests of goodness-of-fit developed by Rayner and Best to the study of the non-Gaussianity of interferometric observations of the cosmic microwave background (CMB). The interferometric measurements (visibilities) are transformed into signal-to-noise ratio eigenmodes, and then the method is applied directly in Fourier space. This transformation allows us to perform the analysis in different subsets of eigenmodes according to their signal-to-noise ratio level. The method can also deal with non-uniform or incomplete coverage of the UV plane. We explore here two possibilities: we analyse either the real and imaginary parts of the complex visibilities (Gaussianly distributed under the Gaussianity hypothesis) or their phases (uniformly distributed under the Gaussianity hypothesis). The power of the method in discriminating between Gaussian and non-Gaussian distributions is studied by using several kinds of non-Gaussian simulations. On the one hand, we introduce a certain degree of non-Gaussianity directly into the Fourier space using the Edgeworth expansion, and afterwards the desired correlation is introduced. On the other hand, we consider interferometric observations of a map with topological defects (cosmic strings). To these previous non-Gaussian simulations we add different noise levels and quantify the required signal-to-noise ratio necessary to achieve a detection of these non-Gaussian features. Finally, we have also studied the ability of the method to constrain the so-called non-linear coupling constant fNL using χ2 simulations. The whole method is illustrated here by application to simulated data from the Very Small Array interferometer.