The deceased, identified as Sushilamma (55) and Sundaramma (45), were working near the tree, police said.
The deceased were tending the tree, which was worshipped by people and tourists, for the last several years and working for the temple situated in Mysore Palace premises, they said.
District incharge Minister V Srinivas Prasad visited the spot and announced a compensation of 1.5 lakh to the next of kin of the deceased.
The injured have been admitted to a city hospital and are recovering, police said.