Yttrium is an element of critical importance for industry and technology. Cyanobacteria Arthrospira platensis was employed for Y(III) recovery from contaminated wastewater through biosorption and bioaccumulation processes. The effect of pH of a solution, contact time, temperature, and initial Y(III) concentration on the adsorption behaviour of Arthrospira platensis were studied. The maximum adsorption capacity of 719.8 mg/g was attained at a pH of 3, temperature of 20 °C, and adsorption time of 3 min. The Langmuir and Freundlich isotherm models were suitable to describe the equilibrium of the biosorption, while kinetic of the process followed the pseudo-first-order model. Thermodynamic parameters showed that the biosorption process was spontaneous and exothermic in nature. In bioaccumulation experiments, Arthrospira platensis was able to remove up to 70% of Y(III) from the solution. Beside biomass uptake capacity, the toxic effect of Y(III) on the biomass productivity and biochemical composition was assessed. Thus, Y(III) in concentration of 10–30 mg/L led to a decrease in the content of proteins, carbohydrates, and phycobiliproteins in the biomass and had no significant negative impact on productivity and photosynthetic pigments content. Experiments performed using Arthrospira platensis showed that biological objects have a great potential to be applied for the recovery of rare earth elements from wastewater.