We study $mathrm{AdS}_3times S^3/mathbb{Z}_ktimes {tilde S}^3/mathbb{Z}_{k}$ 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 $mathrm{AdS}_7/mathbb{Z}_ktimes {tilde S}^3/mathbb{Z}_{k}$, 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 $mathrm{AdS}_3times S^3/mathbb{Z}_ktimes S^2 times Sigma_2$ 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 $mathrm{AdS}_7/mathbb{Z}_k$ solution to massless IIA. Finally, in the massive case, we show that the recently constructed $mathrm{AdS}_3times S^2times mathrm{CY}_2$ solutions with $mathcal{N}=(0,4)$ supersymmetries gain a defect interpretation when $mathrm{CY}_2=T^4$ as surface CFTs originating from D2-NS5-D6 defects embedded within the 5d CFT dual to the Brandhuber-Oz $mathrm{AdS}_6$ background.
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