The expectation is for the Nets to see how his hamstring responds over the next several days.
"He has high hopes and he wants to be back ASAP," Nets coach Steve Nash said on Sunday. "Now, I think we want to protect James, too. We want to make sure he's right.
"This is playoff time. This is time to take some risks, but it has to be right to take those risks -- we're not going to take any old risk. So, we hope he's back. He believes he can be back. But, we've got to see what happens and only can time can tell how he responds."
The Nets, who lead the series 1-0, will also be without Jeff Green in Game 2. Green has missed over a week with a plantar fascia strain in his left foot, but Nash says that he is "progressing nicely."
"I think we'll see him in this series," Nash said. "And hopefully, it's Game 3. But who knows."
The play that Harden appeared to injure himself on was fairly unremarkable -- a simple drive against Bucks guard Jrue Holiday. But when he lobbed a pass, Harden landed and came away from the play grabbing his right hamstring. Harden eventually left the court and struggled as he walked back to the Nets' locker room.
A team spokesperson told ESPN that Harden left the arena shortly afterward to go get an MRI on his hamstring.
"I didn't realize what had happened until he had started walking off the court but we supposed to run a play and he wasn't in his spot and I looked at him, he was grimacing," Kevin Durant said on Saturday. "It just sucks. It sucks. It sucks because I want him to be out there.
"I know how much he cares. I know how much he wants to be in this moment. It sucks. Wishing him a speedy recovery. Keep him involved as much as possible. It's just a bad break."
In the regular season, Harden missed over a month with a right hamstring strain. At first, he missed two games in April with hamstring tightness and the initial imaging didn't show any structural issues, the team said at the time.
Harden came back and played five minutes in a game on April 5 before leaving for the locker room. An MRI revealed a right hamstring strain and he went on to miss the next 18 games. Similarly to in the regular season, Nash said that this time around, the MRI didn't show any structural damage.
Harden was a vocal participant in the Nets' film session on Sunday, his teammate Joe Harris said. Harris described Harden, who did not speak to reporters on Sunday, as "in good spirits."
"We obviously are desperate for him to return," Nash said of Harden. "He's a huge piece of what we do in our team. He's had such a up-and-down recent history with (his hamstring) that it's really hard to predict. And so let's hope for the best."