A method of making a sheet-shaped oxygen absorber includes preparing an oxygen-absorbing resin sheet having opposed first and second surfaces and including an oxygen-absorbing composition in a thermoplastic resin; applying first and second covering members to and in contact with the first and second surfaces, respectively, of the oxygen-absorbing resin sheet to form a laminated structure, at least one of the covering members being air-permeable; and ultrasonically heat sealing the first covering member to the second covering member along the periphery of a closed planar geometric figure, encapsulating at least a part of the oxygen-absorbing resin sheet and cutting the first and second covering members where the first and second covering members are sealed to each other, along the periphery of the closed planar geometric figure, to produce the sheet-shaped oxygen absorber.