Context. Several sugar-like molecules have been found in the interstellar medium (ISM). The molecule studied in this work, 2-hydroxyprop-2-enal, is among the candidates to be searched for, as it is a dehydration product of C 3 sugars and contains structural motifs that are typical for some interstellar molecules. Furthermore, it has recently been predicted that it is more abundant in the ISM than its tentatively detected isomer 3-hydroxypropenal. Aims. So far, only low-frequency microwave data of 2-hydroxyprop-2-enal have been published. The aim of this work is to deepen our knowledge about the millimetre-wave spectrum of 2-hydroxyprop-2-enal, enabling its detailed search towards astronomical objects. In particular, we target the solar-type protostar IRAS 16293-2422 and the star-forming region Sagittarius (Sgr) B2(N). Methods. The rotational spectrum of 2-hydroxyprop-2-enal was measured and analysed in the frequency regions of 128-166 GHz and 285-329 GHz. The interstellar exploration towards IRAS 16293-2422 was based on the Atacama Large Millimeter/submillimeter Array (ALMA) data of the Protostellar Interferometric Line Survey (PILS). We also used the imaging spectral line survey ReMoCA performed with ALMA towards Sgr B2(N) to search for 2-hydroxyprop-2-enal in the ISM. We modelled the astronomical spectra under the assumption of local thermodynamic equilibrium (LTE). Results. We provide laboratory analysis of hundreds of rotational transitions of 2-hydroxyprop-2-enal in the ground state and the lowest lying excited vibrational state. We report its non-detection towards IRAS 16293 B. The 2-hydroxyprop-2-enal/3-hydroxypropenal abundance ratio is estimated to be ≲0.9–1.3, in agreement with the predicted value of ~1.4. We report the non-detection of 2-hydroxyprop-2-enal towards the hot molecular core Sgr B2(N1), and we did not detect the related aldehydes 2-hydroxypropanal and 3-hydroxypropenal either. We find that these three molecules are at least nine, four, and ten times less abundant than acetaldehyde in this source, respectively. Conclusions. Despite the non-detections of 2-hydroxyprop-2-enal, the results of this work represent a significant improvement on previous investigations in the microwave region and meet the requirements for further searches for this molecule in the ISM.