Curry, who is scheduled to participate in Sunday's All-Star Game, rested Thursday on the second night of a back-to-back. It was the second game he missed this season.
Green missed Thursday's game as he continues to recover from a sprained left ankle suffered in Sunday's loss to the Los Angeles Lakers.
Warriors coach Steve Kerr said it was a "very easy" decision to sit his two stars. On the second night of a tough back-to-back, neither Curry nor Green flew with the Warriors to Phoenix in advance of the game.
"Draymond, we definitely didn't want playing a back to back on the ankle from the other night. And Steph just needs a rest," Kerr said before Thursday's game. "This was a brutal, brutal back to back. We got to the hotel at about 3:30 in the morning, and I think given the All-Star break is here and Steph otherwise isn't getting much of one given that he's playing in the game, it made a lot of sense to send him home and just get him an extra day to rest and prepare for the second half of the season."
Kerr said the decision to sit Curry was made about a week ago in recognition of the fact that Curry would be participating in Sunday's All-Star Game and 3-point contest in Atlanta. Green initially injured his ankle in Sunday's loss to the Los Angeles Lakers.
"Well, Steph, we looked at the schedule maybe a week ago and figured that this was what we were going to do," Kerr said. "And then Draymond's was more based on the injury that he suffered in LA."
The Warriors' game against the Suns was originally scheduled for Jan. 15 but had to be rescheduled for Thursday because of COVID-19 protocols. The postponement created a difficult back-to-back after Wednesday's loss to the Portland Trail Blazers with the Warriors arriving early Thursday morning into Phoenix.
Kerr demurred when asked if Curry would have played Thursday had there been no All-Star Game.
"I never gave that any consideration," Kerr said. "Because there is an All-Star Game so that's all we thought about. There's no point in looking at other scenarios that don't exist."
This marks the second game of the season Curry has missed and the sixth missed game for Green. Kelly Oubre, Jr. will miss his second straight game because of a sprained left wrist. Oubre suffered the injury in Tuesday's practice after going up for a dunk and landing awkwardly.