Discovery of the first interstellar asteroid (ISA) - 1I/2017 'Oumuamua - raised a number of questions regarding its origin. Many of them relate to its lack of cometary activity, suggesting refractory composition of 'Oumuamua. Here we explore the possibility that 'Oumuamua-like ISAs are produced in tidal disruption events (TDEs) of refractory planetoids (asteroids, dwarf planets, etc.) by the white dwarfs (WDs). This idea is supported by existing spectroscopic observations of metal-polluted WDs, hinting at predominantly volatile-poor composition of accreted material. We show that such TDEs sourced by realistic planetary systems (including a population of >1000 km planetoids and massive perturbers - Neptune-to-Saturn mass planets) can eject to interstellar space up to 30% of planetary mass involved in them. Collisional fragmentation, caused by convergent vertical motion of the disrupted planetoid's debris inside the Roche sphere of the WD, channels most of the original mass into 0.1-1 km fragments, similar to 'Oumuamua. Such size spectrum of ISAs (very different from the top-heavy distributions expected in other scenarios) implies that planetary TDEs can account for a significant fraction (up to ~30% under optimistic assumptions) of the ISAs. This figure is based on existing observations of WD metal pollution and accounts for observational biases by using realistic models of circum-WD planetary systems. ISAs should exhibit kinematic characteristics similar to old, dynamically hot Galactic populations; we interpret 'Oumuamua's slow Galactic motion as a statistical fluctuation. ISA ejection in individual planetary TDEs is highly anisotropic, resulting in large fluctuations of their space density. We also show that other ISA production mechanisms involving stellar remnants - direct ejection by massive planets around WDs and SN explosions - have difficulty explaining 'Oumuamua-like ISAs.