Desmond's wife, Chelsey, gave birth Tuesday to the couple's first son, Grayson Wesley Desmond.
Manager Jim Riggleman says he expects Desmond to miss two games.
Bernadina was hitting .267 with one home run and two RBIs in 13 games with Syracuse.
Riggleman also says that third baseman Ryan Zimmerman is playing some catch and doing some running. Zimmerman is on the 15-day disabled list with a strained abdominal muscle and hasn't played since April 9.
Riggleman said Zimmerman will probably have a rehabilitation assignment before returning to the big league club.