The generation of convective flow by a chemical wave was studied experimentally on a mm-sized droplet of Belousov-Zhabotinsky (BZ) reaction medium. A propagating chemical wave causes a transient increase in interfacial tension, and this local change in interfacial tension induces convection. The observed flow profile was reproduced with a numerical simulation by introducing the transient increase in interfacial tension to a modified Navier-Stokes equation coupled with a chemical kinetic equation; a modified Oregonator. We also observed the periodic motion of a BZ droplet floating on an oil phase. Such periodic motion is attributed to the rhythmic change in interfacial tension. The observed periodic convective motion coupled with a chemical reaction is discussed in relation to chemo-mechanical energy transduction under isothermal conditions.