No. The MLB The Show series began on PS2 with MLB 06 The Show (2006) and ended on PS2 with MLB 11 The Show (2011). MLB 12 The Show (2012) was PS3-exclusive—the series moved to PS3 permanently that year.
PS2 titles in the series:
For MLB 12 and later, you need a PlayStation 3, 4, or 5.