Identifying and quantifying irreducible and reducible uncertainties in the Antarctic Ice Sheet response to future climate change is essential for guiding mitigation and adaptation policy decision. However, the impact of the irreducible internal climate variability, resulting from processes intrinsic to the climate system, remains poorly understood and quantified. Here, we characterise both the atmospheric and oceanic internal climate variability in a selection of three CMIP6 models (UKESM1-0-LL, IPSL-CM6A-LR and MPI-ESM1.2-HR) and estimate their impact on the Antarctic contribution to sea level over the 21^st century under the SSP2-4.5 scenario. To achieve this, we use a standalone ice-sheet model driven by the ocean through parameterised basal melting and by the atmosphere through emulated surface mass balance estimates. Internal climate variability affects the Antarctic contribution to changes in sea level until 2100 by 45 % to 93 % depending on the CMIP6 model. This may be a low estimate as the internal climate variability in the CMIP models is likely underestimated. For all the three climate models and for most Antarctic regions, the effect of atmospheric internal climate variability on the surface mass balance overwhelms the effect of oceanic internal climate variability on the dynamical ice-sheet mass loss by more than a factor of 3. The atmospheric internal climate variability is similar in the three CMIP6 models analysed in this study. Conversely, the amplitude of oceanic internal climate variability around Antarctica strongly depends on the climate model as underestimated convection, due to either biases in the sea-ice behaviour or in the ocean stratification, leads to weak mid-depth ocean variability. We then issue recommendations for future ice-sheet projections: use several members in the run and in its initialisation, favor 50-year averages to correct or weight simulations over the present-day period, and couple ice-sheet and climate models.