Sources told ESPN's Adrian Wojnarowski that Smart had an MRI on the foot Monday that came back clean, and that Smart will test the foot Tuesday.
"He took a pretty bad fall, got bent up. He has a midfoot sprain, and it's pretty tender and sore right now," Udoka said during a teleconference with the media Monday afternoon ahead of the team's flight to Miami for Game 1 Tuesday night. "We'll get him round the clock treatment and right now he'll be listed as questionable."
Center Robert Williams III, meanwhile, didn't play in Sunday's win. Udoka said before the game both that Williams was available and that he didn't want to disrupt his rotation.
He said Monday that Williams will have no restrictions heading into the series against the Heat, and that it will be easier to integrate him at the start of a series than to try to in the middle of an ongoing one.
"Rob is available, just like he was last night. I mentioned he'd be on a needed basis, and he's available, no minutes restriction. I'm always going to be a little bit cautious with guys coming off a layoff without touching the court, but it's a little bit different starting a new series as opposed to being injected into a Game 7 or Game 6 or whatever the case was before. But he's available, looking better every day, and getting more confident in that."
Williams has blossomed into a huge part of Boston's team this season, playing 61 games while averaging 10 points and 9.6 rebounds -- all career-highs. But he missed the end of the regular season and the beginning of the playoffs after undergoing surgery on his left knee, and then missed time against Milwaukee with a bone bruise in the same knee.
Regardless of the status of Smart and Williams, the Celtics will have to simply plow forward and prepare for what lies ahead against the Heat -- a near carbon copy of the Celtics, with their burly defense and elite wing scoring from Jimmy Butler.
After going up against the Bucks, however, the Celtics say they are ready for whatever comes their way.
"It's the playoffs, and I feel like the deeper that you go, it's more intense, it's physical," Horford said. "Even though the first round was very physical for us, it's not going to be any different. Both teams play hard, but both teams defensively are our tops in the league, or one of the best for sure. So that's what it is at this point. It's just a given that both teams are going to go hard."