Tatis apparently suffered the injury early in the offseason and felt it when he began preparing for spring training, Preller said.
Reports surfaced in December that Tatis suffered scrapes on his hand and knee in a motorcycle accident in his native Dominican Republic.
The injury is a blow to a team that was looking for a fresh start following a brutal late-season collapse that left them with yet another losing record.
Tatis, 23, had a series of injuries to his left shoulder last year, when he still led the NL with 42 home runs in 130 games and finished third in balloting for the NL MVP.
The electrifying Tatis batted .282 with 97 RBIs and 25 stolen bases last year. His season also included two trips to the injured list with left shoulder issues and a trip to the COVID-19 injury list.
He signed a $330 million, 14-year contract with the Padres during spring training last year.