The two All-Stars were arrested April 22 on suspicion of assault after they fought in a home they recently bought. Griner and Johnson got married last week in Phoenix.
The league on Friday cited the integrity of the game in handing down the punishment.
Griner has entered a diversion agreement in which she pled guilty to disorderly conduct and will attend 26 weeks of domestic violence counselling. All charges will be dismissed if she completes her counselling.
Johnson's case has been transferred to a county court and is pending.