The fluid found in the innermost part of mitochondria is called the mitochondrial matrix. The mitochondrial matrix is a viscous fluid that contains the mitochondria's DNA an … d ribosomes.he fluid inside a Cell is called cytoplasm. It serves as a medium were organelles such as vesicles, mitochondria and the Golgi Apparatus are ins … ide, providing the cell with Life's needs; [ALSO the major ingredient of the fluid inside cells is (WATER)]. + 23 others found this useful. Sanjeev Mahajan.