Kambli was taken ill in Mumbai on Friday while he was driving from Chembur to Bandra and suddenly stopped the vehicle.
A policewoman on duty, Sujata Patil noticed he could not drive and arranged to rush him to Lilavati Hospital.
"He is in the intensive care unit and we are monitoring his medical parameters," hospital director Narendra Trivedi told reporters. "He is stable and there is nothing to worry about."
Kambli's wife, Andrea, also issued a statement saying he was "stable and recovering well".
Kambli had previously undergone angioplasty in July last year.
The flashy Mumbaikar played 17 Tests for India and averaged 54.20, which incidentally is higher than the average of his childhood friend Sachin Tendulkar.
His average in first class cricket is also impressive at 59.67, again higher than Sachin's.
Kambli had a longer career in the shorter format of the game, playing 104 ODIs and averaging 32.59.