Transverse-momentum (p_T) differential yields of electrons from semileptonic heavy-flavour hadron decays have been measured in the most central (0–10%) and in semi-central (20–40%) Pb–Pb collisions at sNN=2.76 TeV. The corresponding production cross section in pp collisions has been measured at the same energy with substantially reduced systematic uncertainties with respect to previously published results. The modification of the yield in Pb–Pb collisions with respect to the expectation from an incoherent superposition of nucleon-nucleon collisions is quantified at mid-rapidity (|y| < 0.8) in the p_T interval 0.5–3 GeV/c via the nuclear modification factor, R_AA. This paper extends the p_T reach of the R_AA measurement towards significantly lower values with respect to a previous publication. In Pb–Pb collisions the p_T-differential measurements of yields at low p_T are essential to investigate the scaling of heavy-flavour production with the number of binary nucleon-nucleon collisions. Heavy-quark hadronization, a collective expansion and even initial-state effects, such as the nuclear modification of the Parton Distribution Function, are also expected to have a significant effect on the measured distribution.