The news was announced by the NHL's Department of Player Safety.
Nash left the game after the hit and did not return, telling reporters he had a "headache" from Stuart's head shot.
"It just didn't feel right," Nash said. "Any time you get a head shot, you're concerned. It's not a good feeling."
Stuart will forfeit $55,384.62, per the rules of the collective bargaining agreement. He is not eligible to return until the Sharks face the Stars on Oct. 17.
Although Stuart has "no applicable history," according to a video released by the Department of Player Safety, the Sharks veteran "unnecessarily extends the left side of his body upward -- specifically his left shoulder -- in a way that makes Nash's head the main point of contact, causing an injury."
Information from The Associated Press was used in this report.