White, who is 4-1 with a 2.54 ERA in 48 appearances this season, hurt his toe while accidentally kicking the corner of a bed, a team spokesman said.
Rijo had been on the DL since early June with soreness in his pitching shoulder.
Rijo is 4-3 with a 5.21 ERA in 13 games, including eight starts. The 37-year-old righthander returned to the major leagues late last season after a six-year absence due to numerous surgeries on his pitching elbow.
Celebrity Families of 2014 [PHOTOS]