Kapoor, 67, was admitted to the Breach candy Hospital in south Mumbai after he complained of giddiness and breathlessness, hospital sources said.
The third son of Prithviraj Kapoor, Shashi or Balbirraj, was born in March 1938 in Calcutta.
The youngest sibling of equally well-known actors Raj and Shammi, the handsome Shashi charmed the country during the 1960s and 1970s with blockbusters like "Sharmilee", "Kanyadaan" and "Deewar".
Yash Chopra's "Deewar" (1975) won him the national best supporting actor award.