We study AdS3 times {S}^3/{mathrm{mathbb{Z}}}_ktimes {tilde{S}}^3/{mathrm{mathbb{Z}}}_{k^{prime }} solutions to M-theory preserving mathcal{N} = (0, 4) supersymmetries, arising as near-horizon limits of M2-M5 brane intersections ending on M5’-branes, with both types of five-branes placed on A-type singularities. Solutions in this class asymptote locally to AdS7 /{mathrm{mathbb{Z}}}_ktimes {tilde{S}}^3/{mathrm{mathbb{Z}}}_{k^{prime }} , and can thus be interpreted as holographic duals to surface defect CFTs within the mathcal{N} = (1, 0) 6d CFT dual to this solution. Upon reduction to Type IIA, we obtain a new class of solutions of the form AdS3× S3/ℤk× S2×Σ2 preserving (0,4) supersymmetries. We construct explicit 2d quiver CFTs dual to these solutions, describing D2-D4 surface defects embedded within the 6d (1,0) quiver CFT dual to the AdS7/ℤk solution to massless IIA. Finally, in the massive case, we show that the recently constructed AdS3× S2× CY2 solutions with mathcal{N} = (0, 4) supersymmetries gain a defect interpretation as surface CFTs originating from D2-NS5-D6 defects embedded within the 5d CFT dual to the Brandhuber-Oz AdS6 background.