Abstract The uncertainty principle for a two-dimensional signal, giving us a lower bound for the product of the spreads (uncertainty product) of the signal representations in two specific Gyrator domains (GDs), is developed and presented. The GDs are defined by the Gyrator transform (GT), which is a new mathematical tool for analysis and processing of two-dimensional signals belonging to the linear canonical transforms. The obtained lower bound for the uncertainty principle depends on the two rotation angles that define the two GDs of the two-dimensional signal. The resulting uncertainty principle could be used in image processing and applications based on the GT. Finally, we show that the uncertainty principle for the antisymmetric Fourier transform with a rotation of the coordinates at π/2 is a special case of the bidimensional uncertainty product associated with two specific GDs.