Starc had surgery last week that required 30 stitches after suffering deep lacerations when he collided with training equipment.
Smith was in the field as the 26-year-old left-armer, who was rested from Australia's one-day series in South Africa later this month, gashed his leg open.
"It wasn't nice at all," Smith told reporters in Sydney.
"It was actually probably one of the most gruesome things I have ever seen.
"I guess for Mitch, he's got no tendon or ligament damage so given everything goes well over the next couple of weeks we're confident that he'll be okay for the first Test match."
Starc, who was Australia's top performer with 24 wickets at 15.16 in the losing three-Test series in Sri Lanka last month, was due to leave hospital on Monday to begin his rehab.
"It wasn't great but I'm sure in a couple of weeks' time he'll be okay and back into things," said Smith.
Australia play South Africa in a three-Test series starting in Perth on November 3.