Hedges, 22, will join the team for Monday night's game against the Giants in San Francisco.
Over 79 plate appearances with Triple A affiliate El-Paso, Hedges was batting .324 with two home runs and 15 RBIs.
A second round pick in 2011, Hedges was ranked San Diego's No. 2 prospect in 2015 by MLB.com.
In a corresponding roster move, backup catcher Wil Nieves has been designated for assignment.
Derek Norris has started the majority of games at catcher for the Padres (14-12), who currently sit in second in the NL West.