The magnetic properties of a three-dimensional infinite network compound, [{Ru₂(m-FPhCO₂)₄}₂(BTDA-TCNQ)] (m-FPhCO₂⁻ = m-fluorobenzoate; BTDA-TCNQ = bis(1,2,5-thiadiazolo)tetracyanoquinodimethane), were investigated under hydrostatic pressures up to 12.9 kbar. The applied pressure caused the intralattice exchange couplings to weaken, inducing a decrease in the magnetic phase transition temperature from 107 K at ambient pressure to 57 K at 12.9 kbar.