Achieving an all-fiber ultra-fast system with above kW average power and mJ pulse energy is extremely challenging. This paper demonstrated a picosecond monolithic master oscillator power amplifier system at a 25 MHz repetition frequency with an average power of approximately 1.2 kW, a pulse energy of approximately 48 μJ and a peak power of approximately 0.45 MW. The nonlinear effects were suppressed by adopting a dispersion stretched seed pulse (with a narrow linewidth of 0.052 nm) and a multi-mode master amplifier with an extra-large mode area; then an ultimate narrow bandwidth of 1.32 nm and a moderately broadened pulse of approximately 107 ps were achieved. Meanwhile, the great spatio-temporal stability was verified experimentally, and no sign of transverse mode instability appeared even at the maximum output power. The system has shown great power and energy capability with a sacrificed beam propagation product of 5.28 mm$\cdot$mrad. In addition, further scaling of the peak power and pulse energy can be achieved by employing a lower repetition and a conventional compressor.