2020 MLB draft: Mock drafts, rankings, order and more Jeff Passan details MLB’s decision to trim the draft from 40 rounds to 5 and how that was perceived around the game. (0:42) While the official start date hasn’t been announced, the 2020 MLB draft is reportedly expected to begin June 10 and be held virtually due to the ongoing coronavirus pandemic. The draft was initially scheduled to be held June 10-12. How many rounds will there be? This year’s draft will be shortened from 40 to five rounds and teams can sign an unlimited number of undrafted players for $20,000.