Bayer Leverkusen centre-back Tah, 20, has been recalled from a holiday in Miami to join up with the world champions, who face Ukraine in Lille in their Group C opener on Sunday.
"I wanted a direct replacement. Jonathan has been in our team before and has been training on his own for the last three weeks," Low said at a press conference at the German squad's base in Evian-les-Bains, near the Swiss border.
Roma defender Rudiger was ruled out of the competition after tearing cruciate ligaments in his right knee on Tuesday in Germany's first training session after arriving in France.
"You may see me struggle, but you will never see me quit! Thx for all your get well soon wishes! #NeverGiveUp", Rudiger tweeted later.
Rudiger had looked set to feature alongside Jerome Boateng in the heart of Germany's defence against Ukraine, with Mats Hummels, who is in the squad, already ruled out for that match with a calf muscle tear.
Tah made his senior debut for Germany in the 3-2 friendly loss to England in Berlin on March 26.
Germany are already without midfielder Ilkay Gundogan and Borussia Dortmund winger Marco Reus due to injury, while Bastian Schweinsteiger has been struggling for fitness.
"We are obviously missing certain players who had an important part to play in my plans," Low added.
"I would have preferred to have available to me the squad I imagined three weeks ago, but it is not the case. I always said we wouldn't start feeling sorry for ourselves.
"We have a very good team, very good players. I have complete confidence in them."