The All-Star forward suffered the injury in the second quarter of the Nuggets' 127-109 loss to the Los Angeles Lakers on Sunday.
"I still don't know how bad it is," Nuggets coach Michael Malone said at shootaround Wednesday. "Just just as thorough as possible, he's going to go talk to some other doctors, get some other opinions before we make a decision to what the best course of action is regarding his left wrist."
Millsap, 32, is averaging 16.0 points, 6.3 rebounds and 3.2 assists in his first season with the Nuggets.
"I told the team this morning, obviously it's unfortunate when any player goes down, but I go, 'That injury is not going to define us or our season.' We're going to continue to prepare, to work, to fight and to compete," Malone said.
"The great thing about having a deep roster and a deep frontcourt is other guys are ready to take advantage of those minutes. I feel awful for Paul Millsap. We'll wait to see what the best course of action is, but while he is out, in his stead other guys have to step up and the season must go on."
The Vertical first reported that Millsap would need surgery.
ESPN's Tim MacMahon contributed to this report.