From the mlb.com transaction page for this month:
3/15: Seattle Mariners placed LHP Ryan Feierabend on the 60-day disabled list.
So, teams can start doing it now. On that same page, you can see the transactions from previous years, and looking at March of last year, the first one was on 3/12, a few here and there, and then a bunch starting on 3/20 through the end of the month.
Hope that helps.