Scale-invariance and diverging length scales are the hallmark of critical systems, the study of which can provide insights into its relation to critical universality classes. In neuroscience, the brain criticality hypothesis has motivated the characterization of cerebral activity using avalanche scaling exponents and long-range temporal correlations. In non-invasive brain recording modalities, the degree of spatial coarse-graining that occurs at the sensor level precludes proper avalanche characterizations, and only the analysis of temporal scale-invariance is possible. Multifractal analysis, which is a higher statistical order extension of the common long-range temporal correlation characterization of scale invariance, has been introduced to extract a full characterization of the temporal scale-invariance of time series. In this contribution, we show that the recently introduced Landau-Ginzburg theory for critical oscillations exhibits multifractal temporal scaling in a neighborhood of its critical point. We compare two approaches used in literature based on observing either the low-frequency fluctuations or the amplitude envelope of the oscillatory process, and show that they correspond to fundamentally different processes. This work provides a currently missing critical modeling basis for interpreting multifractality in electrophysiological brain recordings.