Dust grains can be efficiently accelerated and shattered in warm ionized medium (WIM) because of the turbulent motion. This effect is enhanced in starburst galaxies, where gas is ionized and turbulence is sustained by massive stars. Moreover, dust production by Type II supernovae (SNe II) can be efficient in starburst galaxies. In this paper, we examine the effect of shattering in WIM on the dust grains produced by SNe II. We find that although the grains ejected from SNe II are expected to be biased to large sizes ($a\ga 0.1 \micron$, where $a$ is the grain radius) because of the shock destruction in supernova remnants, the shattering in WIM is efficient enough in $∼ 5$ Myr to produce small grains if the metallicity is nearly solar or more. The production of small grains by shattering steepens the extinction curve. Thus, steepening of extinction curves by shattering should always be taken into account for the system where the metallicity is solar and the starburst age is typically larger than 5 Myr. These conditions may be satisfied not only in nearby starbursts but also in high redshift ($z>5$) quasars. Comment: 12 pages, 11 figures, accepted for publication in MNRAS