Context. Spectral lines of minor isotopic species of molecules that are abundant in space may also be detectable. Their respective isotopic ratios may provide clues about the formation of these molecules. Emission lines of acetone in the hot molecular core Sagittarius B2(N2) are strong enough to warrant a search for its singly substituted ¹³C isotopologs. Aims. We want to study the rotational spectra of CH₃¹³C(O)CH₃ and ¹³CH₃C(O)CH₃ and search for them in Sagittarius B2(N2). Methods. We investigated the laboratory rotational spectrum of isotopically enriched CH₃¹³C(O)CH₃ between 40 GHz and 910 GHz and of acetone between 36 GHz and 910 GHz in order to study ¹³CH₃C(O)CH₃ in natural isotopic composition. In addition, we searched for emission lines produced by these species in a molecular line survey of Sagittarius B2(N) carried out with the Atacama Large Millimeter/submillimeter Array (ALMA). Discrepancies between predictions of the main isotopic species and the ALMA spectrum prompted us to revisit the rotational spectrum of this isotopolog. Results. We assigned 9711 new transitions of CH₃¹³C(O)CH₃ and 63 new transitions of ¹³CH₃C(O)CH₃ in the laboratory spectra. More than 1000 additional transitions were assigned for the main isotopic species. We modeled the ground state data of all three isotopologs satisfactorily with the ERHAM program. We find that models of the torsionally excited states v₁₂ = 1 and v₁₇ = 1 of CH₃C(O)CH₃ improve only marginally. No transitrrrion of CH₃¹³C(O)CH₃ is clearly detected toward the hot molecular core Sgr B2(N2). However, we report a tentative detection of ¹³CH₃C(O)CH₃ with a ¹²C/¹³C isotopic ratio of 27 that is consistent with the ratio previously measured for alcohols in this source. Several dozens of transitions of both torsional states of the main isotopolog are detected as well. Conclusion. Our predictions of CH₃¹³C(O)CH₃ and CH₃C(O)CH₃ are reliable into the terahertz region. The spectrum of ¹³CH₃C(O)CH₃ should be revisited in the laboratory with an enriched sample. The torsionally excited states v₁₂ = 1 and v₁₇ = 1 of CH₃C(O)CH₃ were not reproduced satisfactorily in our models. Nevertheless, transitions pertaining to both states could be identified unambiguously in Sagittarius B2(N2).