The Thunder announced Thursday that Hartenstein suffered a non-displaced fracture in his left hand and will be re-evaluated in 5-6 weeks, Shams Charania of ESPN reports.
Hartenstein delivered 11 points (4-7 FG, 3-7 FT), three rebounds, three assists, a steal and a block across 21 minutes in Tuesday's 124-94 preseason win over the Nuggets.
Hartenstein will crack the starting lineup in Tuesday's preseason game against Denver.
Hartenstein posted six points (2-3 FG, 2-4 FT), nine rebounds, three assists, a steal and a block across 15 minutes off the bench in Wednesday's 122-113 preseason loss to the Rockets.
Hartenstein won't start Monday's preseason game against the Spurs, Rylan Stiles of FanSided.com reports.
Hartenstein and the Thunder agreed to a three-year, $87 million contract Monday, Shams Charania of The Athletic reports.
Hartenstein contributed four points (1-3 FG, 2-2 FT), seven rebounds, six assists and one steal over 33 minutes during Friday's 116-103 loss to Indiana in Game 6 of the Eastern Conference Semifinals.
Hartenstein contributed seven points (2-3 FG, 3-4 FT), 15 rebounds, five assists and one block over 31 minutes in Tuesday's 121-91 win over the Pacers in Game 5 of the Eastern Conference Semifinals.
Hartenstein (shoulder) isn't listed on New York's injury report for Tuesday's Game 5 against the Pacers.
Hartenstein suffered a minor shoulder injury in Sunday's loss, but he should be good to go for Game 5, Ian Begley of SportsNet New York reports.