Smith was standing to the side of the Melbourne Cricket Ground nets on Sunday when he was struck by a ball that had been hit by Cameron Bancroft. Smith later had a hit but was in obvious discomfort.
Opener David Warner said Smith was OK and would play in the fourth test. Australia has clinched the Ashes series 3-0.
"There's absolutely nothing wrong with him, he's fine," Warner said.
"He was confused how it actually got there. I think we all were. It hit the top of the rail and then just flicked up."
Smith was struck on the same hand while working on his slips catching at training earlier in the season. Wicket-keeper Tim Paine, who delayed his arrival into Melbourne after his father-in-law had a stroke, trained with the squad today.
"It's a tough time for them. We're doing everything we can to get behind him and support the family," Warner said.
Earlier, team officials said lefthanded fast bowler Mitchell Starc would not play due to a bruised right foot. He will be replaced by Jackson Bird.
First Published: December 24, 2017, 11:23 AM IST