Lahm announced his retirement from international football on Friday after having captained his country to World Cup glory this summer.
Low, who signed a two-year extension to his contract prior to the World Cup, has been rumoured to be considering his own position after taking the final step at a major tournament following three previous near-misses.
Niersbach has dismissed that speculation, however, and stated he fully expects Low to remain in charge up to Euro 2016, and beyond.
"Everything has been cleared and it is obvious who will be sitting on our bench when we play Argentina, again, on September 3," Niersbach said at a meeting of the Bavarian Football Association, according to Kicker magazine.
"We don't need to worry at all about the national team coach."
Niersbach believes Low can emulate Vicente del Bosque by leading Germany to the European Championships' title in two years' time, like Spain did in 2010 and 2012.
"That is also Joachim Low's aim," added Niersbach.