Griner has appeared in 20 of 23 games for Phoenix in her first season since her high-profile detainment in Russia last year, which lasted nearly 10 months.
"The Mercury fully support Brittney and we will continue to work together on a timeline for her return," a statement from the team said.
Griner has been a bright spot for an otherwise struggling Mercury team that currently sits 10th in the WNBA standings at 6-17. The 6-foot-9 center has averaged 18.2 points, 6.7 rebounds and 1.7 blocks per game, leading Phoenix in each of those categories, and earned her ninth All-Star selection last month.
Wins over eighth-place Chicago and 11th-place Indiana would help Phoenix gain ground in securing a postseason bid. The Mercury haven't missed the playoffs since 2012.
While the Mercury will be without Griner this road trip, guard Diana Taurasi is off the injury report after being sidelined with a quad contusion and left big toe injury. Taurasi, the WNBA's all-time leading scorer, has appeared in 16 games this summer and is 71 points away from hitting 10,000 career points.