In this manuscript, we investigate the influence of the extended uncertainty principle (EUP) on the thermodynamics of a charged rotating Bañados, Teitelboim and Zanelli (BTZ) black hole in (2+1)-dimensional anti-de Sitter (AdS) and de Sitter (dS) space-time, respectively. We find that EUP-corrected Hawking temperature, entropy, volume, Gibbs free energy, pressure and heat capacity functions have different characteristic behaviours in (A)dS space-time. During the detailed analysis, we obtain a critical horizon in the AdS space-time where the pressure has a non-zero minimum value. However, in the dS space-time, we cannot achieve such a minimal pressure value. Instead there is a "cut point" where the pressure becomes zero. We show that after that horizon value the black hole becomes unstable, with negative pressure which leads to the collapse of the black hole.