Shanahan said Friday that Haynesworth had departed to join his family in Nashville.
"Obviously, what he's going through right now is paramount," Shanahan told reporters. "We're giving him and his family all of our prayers and thoughts. I think that's the main concern right now."
The coach said it would be unfair to ask a player about playing a game after such a family tragedy.
Lance McCoy, 23, was speeding Thursday night when he collided with a car pulling out of a parking lot. Police said a preliminary investigation found McCoy's excessive speed was the main cause of the crash.
The car's driver, Benjamin Smith, 27, of Nashville, told police he didn't see the motorcycle until impact.
Haynesworth is a former Tennessee Titan. His half-brother was from Madison, about seven miles north of Nashville.
Haynesworth's agent said Friday that he had no comment.
South Carolina Sen. Gerald Malloy, a close family friend, told The Associated Press that it was a very difficult time for the family.
"I would hope everyone gives them time to deal with a very personal matter for a young man whose life has been cut short by this tragedy," Malloy said.
Shanahan said Haynesworth's backup at nose tackle, Anthony Bryant, is ready to return after missing the last two games with a concussion and that rookie left tackle Trent Williams also is OK to play after being sidelined for two games with toe and knee injuries.
The Associated Press contributed to this report.