The ALICE Collaboration reports the first fully-corrected measurements of the N-subjettiness observable for track-based jets in heavy-ion collisions. This study is performed using data recorded in pp and Pb-Pb collisions at centre-of-mass energies of s = 7 TeV and sNN = 2.76 TeV, respectively. In particular the ratio of 2-subjettiness to 1-subjettiness, τ₂/τ₁, which is sensitive to the rate of two-pronged jet substructure, is presented. Energy loss of jets traversing the strongly interacting medium in heavy-ion collisions is expected to change the rate of two-pronged substructure relative to vacuum. The results are presented for jets with a resolution parameter of R = 0.4 and charged jet transverse momentum of 40 ≤ p_T,jet ≤ 60 GeV/c, which constitute a larger jet resolution and lower jet transverse momentum interval than previous measurements in heavy-ion collisions. This has been achieved by utilising a semi-inclusive hadron-jet coincidence technique to suppress the larger jet combinatorial background in this kinematic region. No significant modification of the τ₂/τ₁ observable for track-based jets in Pb-Pb collisions is observed relative to vacuum PYTHIA6 and PYTHIA8 references at the same collision energy. The measurements of τ₂/τ₁, together with the splitting aperture angle ∆R, are also performed in pp collisions at s = 7 TeV for inclusive jets. These results are compared with PYTHIA calculations at s = 7 TeV, in order to validate the model as a vacuum reference for the Pb-Pb centre-of-mass energy. The PYTHIA references for τ₂/τ₁ are shifted to larger values compared to the measurement in pp collisions. This hints at a reduction in the rate of two-pronged jets in Pb-Pb collisions compared to pp collisions. [Figure not available: see fulltext.]