We have investigated the Shubnikov-de Haas effect in single crystals of the group II-V diluted magnetic semiconductors (Cd_1-x-yZn_xMn_y)₃As₂ (x + y = 0.3, y = 0.06 and 0.08) at temperatures T = 4.2 to 16 K and magnetic fields B = 0 to 6.5 T under hydrostatic pressure p up to 14 kbar. Values of the cyclotron mass m_c, the effective g-factor g*, and the Dingle temperature T_D have been determined. In both specimens a linear field dependence m_c(B) = m*_c + aB is observed, where m*_c is independent of B but increases with pressure and where a does not depend on p and B. Additionally, pressure dependencies of g*, T_D and the Hall mobility μ_R are observed. The dependence of m*_c and g* on p is interpreted within the three-band Kane model. The decrease of μ_R and T_D with increasing pressure is consistent with an increase of m*_c.