Snell left Friday night's 120-108 win over Chicago in the third quarter with the injury and did not return.
The Hawks say tests confirmed the ankle sprain and also showed a bone bruise. Snell remained in Atlanta and will miss road games at Charlotte and against Toronto in Tampa on Tuesday night.
Snell's status will be updated following the team's return to Atlanta.
Snell is averaging 5.5 points and 2.4 rebounds in a reserve role.