Grizzlies' guard Morant went down in the fourth quarter with a right-hand injury in a 128-112 home loss to the Los Angeles Lakers on Sunday.
Greek big man Antetokounmpo suffered a bruised lower back after a first-quarter fall in the top-seeded Bucks' 130-117 home loss to Miami.
Both stars are uncertain to play when their best-of-seven post-season first-round matchups continue on Wednesday.
Bucks coach Mike Budenholzer said Monday that an MRI on Antetokounmpo came back clean.
"He's still sore, but, I think, progress," Budenholzer said. "He's getting some treatment and we will just continue to monitor him for the next day or two.
"Quite fortunate two days between games. Mostly positive. Mostly optimistic. But we'll see how he feels over the next day or two."
Morant, who missed most of March after displaying a gun in a Colorado nightclub, said his latest setback was stressful and that his status for game two was "pretty much in jeopardy".
"I'm going to do anything to try to be out there for my team, be out there on the floor, pretty much how much I can tolerate (so) I can go out there and be somewhat like myself," Morant said after the loss.
"If not, I don't want to do anything to hurt the team."
Antetokounmpo went down after a collision with Miami's Kevin Love (34) and tried to return but was unable to continue.
"That's our guy," said Bucks forward Khris Middleton (31).
"We hope he's going to be well, that he's going to be out there with us on Wednesday.
"We've just got to focus on who is out there. It sucks our guy goes down and can't return but we've still got a job to do out there."
Both players were injured driving to the basket in situations where defenders tried to block their path to induce charging fouls.
Morant leapt high against Lakers' big man Anthony Davis (30) and landed awkwardly on an already-taped right hand, then rose and grabbed his right hand as he ran to the locker room.
While there was concern two stars were lost off similar fouls, Bucks star Jrue Holiday (32) saw no need to try and make a change.
"That's a basketball play," he said. "Any time you jump in the air that's a risk that you take. It's very unfortunate people are getting hurt that way, but I think a charge is a part of basketball."
Memphis forward Jaren Jackson (23) was confident Morant could make a comeback for game two.
"We know how much he cares, how much he puts in. When you go down like that in the fourth quarter it's definitely frustrating," Jackson said.
"He just needs a minute. He's fine. I've seen him battle through pretty much anything."
Next-man-up mindset
Desmond Bane (24) said that if Morant isn't ready, reserve Tyus Jones (26) will be set to face the Lakers.
"You never want to see a teammate go down in pain," Bane said. "But we've been in that position before without him on the floor and Tyus is capable of playing a big role, make plays on both ends of the floor.
"Hopefully he's back Wednesday but if not I think Tyus will be ready to go."
It's a similar mindset for the Bucks, who had the NBA's best regular-season record.
"We don't want (Antetokounmpo) to be hurt but it's still 'next man up mentality' on this team," Holiday said. "We have enough talent to cover for him until he comes back. I just don't want to see him hurt."
