Harden did not practice Thursday and underwent an MRI to determine the severity of the injury, which caused him to exit Wednesday's 100-89 loss to the Utah Jazz with 5:19 remaining.
Harden will be re-evaluated before the Rockets' road trip, which begins Nov. 2. He has been ruled out of Friday's game against the Los Angeles Clippers and Tuesday's game against the Portland Trail Blazers.
Harden, the reigning MVP, missed seven games in January of last season due to a Grade 2 hamstring strain. He was optimistic Wednesday night that this strain was not nearly as severe.
"It's nothing serious, nothing serious," said Harden, who walked out of the Toyota Center without a noticeable limp. "It's nothing close to last year. Just being cautious."
Rockets starting small forward James Ennis III will miss his second consecutive game Friday due to a Grade 2 hamstring strain and has also been ruled out for Tuesday. Coach Mike D'Antoni is considering starting forward Carmelo Anthony for the first time this season against the Clippers.
Houston, which had the NBA's best record at 65-17 last season, has stumbled to a 1-3 start.
"Obviously, we'd love to have the team full strength, but right now we're sort of dealing with the injury bug," Paul said. "We just need to get past it and just hoop, pile up some wins. We'll just try to weather the storm. I'd rather it be now than April or something like that. We'll just try to figure it out."