The news broke on Wednesday that Oswalt had left the team, and there was no timetable for his return.
In a statement, GM Ruben Amaro said "There has been a tremendous amount of tornado activity near Roy's home in Mississippi resulting in several tragic deaths and significant devastation to the area.? Because of this, Roy is concerned about his family's well-being.?"
"He has chosen to take time to make sure there wasn't significant damage to his home, but more importantly, to make certain that his wife and children are okay," the statement continued.
Amaro went on to say that this storm struck almost a year to the day that Oswalt's parents' home was destroyed by a tornado.
Amaro was hopeful Oswalt would be back for his next start, but that the situation is still day-to-day.
Oswalt threw three ineffective innings in a loss to the Arizona Diamondbacks Tuesday night and was long gone from the Philadelphia clubhouse when the game ended.
A source who was in attendance at Chase Field on Tuesday told ESPN.com's Jayson Stark that Oswalt was observed speaking on the phone in the dugout for a long time before the game, suggesting he received news before he pitched that may have precipitated his departure.
Players rarely bring phones onto the field at any point in the day, and many teams actually prohibit that practice.
Oswalt (3-1) allowed five runs on six hits with no strikeouts and one walk. He threw 57 pitches, 36 of them strikes.
The right-hander had given up five runs in 24 innings in his first four starts this season and had not been the losing pitcher since a July 30, 2010, outing at Washington.