Cloyd was placed on the paternity list Monday, Joe Frisaro of MLB.com reports.
It's unclear how long Cloyd will be away from the team at this point. He won't be missed, however, as he's been used primarily as a mop-up man this season, posting a 12.46 ERA across 4.1 innings of work. The move clears room on the roster for Dan Straily, who was activated from the disabled list in a corresponding move.