[Problem] To provide a membrane separation apparatus and a membrane separation method capable of reducing energy consumption,[Solution] A membrane separation apparatus (10) includes: a membrane separator (20) supplied with a fluid (X) containing a component (A) and a component (B) and separating the fluid (X) into a fluid (Y) having a higher concentration of the component (A) than the fluid (X) and a fluid (Z) having a lower concentration of the component (A) than the fluid (X) by using a separation membrane; a first compressor (21) adiabatically compressing the fluid (Y); a first heat exchanger (11) to which the fluid (Y) adiabatically compressed by the first compressor (21) is introduced as a heat source; and a second heat exchanger (12) to which the fluid (Z) is introduced as a heat source. The fluid (X) is divided and conveyed by first and second supply lines (31, 32), the divided fluids (X) are heated by the first and second heat exchangers (11, 12), respectively, then merged and supplied to the membrane separator (20).