Smith, who went to the Pro Bowl last season, suffered the injury after banging his knee during a practice last week. Subsequent swelling led to the Texans re-evaluating his status Monday afternoon.
"We took an aggressive approach to clean it up," Kubiak said. "Everything went good, so now we start the process of coming back. It's going to be a day-to-day deal right now, but he's got some work to do to come back."
When Smith spoke to reporters Monday, he said he was unsure exactly what his injury was. Kubiak said it will be a few days before the Texans know exactly how long Smith will be out.
Second-year guard Ben Jones will play in Smith's place.
Safety Ed Reed was missing from Tuesday morning's practice, as well. Kubiak said Reed is splitting his time between Houston and an out-of-town rehabilitation specialist with whom he's worked before.
"We've got him working with a certain guy who's been working with his rehab that's done it before," Kubiak said. "He's going to spend a couple of days with him. We're going to do it this week and we're going to do it early next week, so that we're proceeding in the right direction in phases of his rehab."
Asked if this meant Reed had a setback in his recovery, Kubiak said no.
Reed, who joined the Texans in free agency from the Baltimore Ravens, had arthroscopic hip surgery in the last week of April and began training camp on the physically unable to perform list.
He has said previously he is hopeful he will be able to play in the first week of the regular season when the Texans face the Chargers in San Diego on "Monday Night Football."