Oswalt returned to Houston on Tuesday. He plans to make his next start as scheduled on Thursday against Cincinnati.
Oswalt's childhood home was destroyed by the tornado Saturday near Weir, Miss. His mother stayed in a closet with her dog as the twister came through.
Oswalt drove home on Saturday and worked with parents to salvage what little they could from the debris. He said many of the homes in the neighborhood where he grew up were destroyed, but that no one was killed in the immediate area.