It was Chelsea who started strongly and Mason Mount dispossessed Ndidi to score his first PL goal on seven minutes.
N'Golo Kante almost doubled their lead but was denied by the outstretched leg of Christian Fuchs.
Leicester grew in confidence after half-time and Ndidi headed in James Maddison's corner on 67 minutes.
Maddison and Youri Tielemans both came close to finding a winner for the Foxes but were unable to find a way past Kepa Arrizabalaga.
Leicester are in 12th place after drawing their first two matches, while Chelsea, in 15th, have one point.
Chelsea: 24 Aug v Norwich (A)
Leicester: 24 Aug v Sheff Utd (A)