The shapes of jets with transverse energies, EjetT, up to 45 GeV produced in neutral- and charged-current deep inelastic e+p scattering (DIS) at Q2 > 100 GeV2 have been measured with the ZEUS detector at HERA. Jets are identified using a cone algorithm in the η-φ plane with a cone radius of one unit. The jets become narrower as EjetT increases. The jet shapes in neutral- and charged-current DIS are found to be very similar. The jets in neutral-current DIS are narrower than those in resolved processes in photoproduction and closer to those in direct-photon processes for the same ranges in EjetT and jet pseudorapidity. The jet shapes in DIS are observed to be similar to those in e+e- interactions and narrower than those in p̄p collisions for comparable EjetT. Since the jets in e+e- interactions and e+p DIS are predominantly quark initiated in both cases, the similarity in the jet shapes indicates that the pattern of QCD radiation within a quark jet is to a large extent independent of the hard scattering process in these reactions.