In vitro plant cell and tissue culture systems allow for controlling a wide range of culture environmental factors selectively influencing biomass growth and the yield of secondary metabolites. Among the most efficient methods, complex supplementation of the culture medium with elicitors, precursors, and other functional substances may significantly enhance valuable metabolite productivity through a stress induction mechanism. In the search for novel techniques in plant experimental biotechnology, the goal of the study was to evaluate stress-inducing properties of novel biodegradable ester-based scaffolds made of poly(glycerol sebacate) (PGS) and poly(lactic acid) (PLA) influencing on the growth and deoxyshikonin productivity of Rindera graeca hairy roots immobilized on the experimental constructs. Rindera graeca hairy roots were maintained under the dark condition for 28 days in three independent systems, i.e., (i) non-immobilized biomass (a reference system), (ii) biomass immobilized on PGS scaffolds, and (iii) biomass immobilized on PLA scaffolds. The stress-inducing properties of the applied polymerized esters selectively impacted R. graeca hairy roots. The PGS scaffolds caused the production of deoxyshikonin, which does not occur in other culture systems, and PLA promoted biomass proliferation by doubling its increase compared to the reference system.