Antonio Conte's men thumped the same side 5-0 two months ago in last season's Europa League semi-finals but w unable to find a way through at the Kiev Olympic Stadium.
Romelu Lukaku had scored in nine straight European matches for Inter and came closest to making the breakthrough, his free-kick being pushed onto the bar by Anatolii Trubin.
Nicolo Barella also struck the crossbar in the first half and Lautaro Martinez missed a glorious opportunity early in the second as Inter followed up last week's 2-2 with Borussia Monchengladbach with another underwhelming point.
Shakhtar held on to stun Real Madrid 3-2 in its opening group game but they had Trubin to thank for keeping it level against Inter.
Barella sent a first-time shot against the frame of the goal from the edge of the 18-yard box after Lukaku had been denied by the teenage keeper.
Lukaku was then left with a look of disbelief on his face nine minutes before the interval as his free-kick was kept out by the fingertips of Trubin, who only turned 19 in August.
The chances continued to fall Inter's way as Trubin parried Marcelo Brozovic's powerful drive into the path of Martinez, who fired the rebound wide from six yards.
Lukaku had a penalty shout rejected for a tug on his shirt from Valerii Bondar as Shakhtar, still without a number of first-team players due to a coronavirus outbreak in the camp, saw out proceedings to secure another impressive European result.