Smart is out with a right ankle sprain while Herro is dealing with a left groin strain. Heat coach Erik Spoelstra said that Herro would be "day-to-day" moving forward.
"We just had to be responsible and take the decision out of his hands," Spoelstra said. "He really wants to be out there tonight. The trainers and Dr. [Harlan] Selesnick don't think that's the best idea just because of the intensity and everything, but we'll see. He's young, we'll treat him day-to-day, and we'll see what happens from here."
Smart suffered his injury in the second half of Game 3 and briefly left the game before returning. Celtics center Robert Williams III, who missed Game 3 with knee soreness, started Tuesday's game.
For the Heat, veteran Victor Oladipo figures to get even more minutes in the short-term with Herro out. Oladipo played well defensively in Saturday's 109-103 Game 3 win, scoring five points and collecting four steals in 20 minutes.
"Obviously, we feel like our depth is one of our biggest strengths," Spoelstra said. "So we have enough guys that can step up."
Heat swingman Jimmy Butler, who sat out the second half of Game 3 because of right knee inflammation, started in Game 4. Spoelstra was asked whether a play midway through the second quarter, by Celtics guard Payton Pritchard, had anything to do with Butler's injury. Pritchard ran into Butler and fell over, then grabbed Butler's right knee to try and slow him down.
"We don't know [if that contributed]," Spoelstra said. "It could have had an effect. It was not a basketball play. We're not really sure why it was determined as that was a basketball play, or that that was a legal play or that was a safe play. We're not going to say it's bigger than it was, 'cause we don't know if that's what triggered Jimmy's injury. But regardless, it should be two separate examples. And we don't need it, we don't care; the league doesn't have to do anything."
Spoelstra said he didn't see the play by Pritchard in the moment, but was alerted to it by the Heat's video staff later.
"We don't care," Spoelstra said. "They can do whatever they want. That has nothing to do with us trying to compete to get to a win. We're not crying. We're not begging for nothing."