V K Birdi, Deputy Inspector General (DIG) of Police, Central Kashmir, told The New Indian Express that the tourist bus came under attack from stone-pelters at Narabal area on Srinagar-Gulmarg road around 11 am.
Thirumani was taken to SKIMS hospital at Soura, where he succumbed to the injuries later, the official added.
The demise of the Chennai tourist comes in the backdrop of a spurt in stone-pelting incidents to protest the counter-militancy operations in South Kashmir.
Thirumani's body was later brought to the police hospital here and Chief Minister Mehbooba Mufti went there immediately after she was informed that the tourist had passed away.
This is the third incident when stone-pelters have attacked innocent civilians in Kashmir.
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"Stone-pelters threw stones on our cab and Thirumani was hit in the head that resulted in his death", Rajwali, father of the deceased, said. "Let's try and wrap our heads around the fact that we stoned a tourist, a guest, to death while we glorify these stone pelters & their methods", he tweeted.
The former chief minister prayed for the recovery of the woman injured in the incident. A case has been registered in the matter.
"Investigations have started to identify the culprits involved in the incident", a police official said.
According to reports, the stone-pelters had been protesting against the killing of 5 Hizbul Mujahideen terrorists in an encounter in Jammu and Kashmir's Shopian on Sunday.
On April 30, seven tourists were injured when stone-throwers targeted vehicles in south Kashmir's Anantnag district. Jammu & Kashmir DGP S P Vaid, while congratulating the forces for neutralising the five militants, had also expressed disappointment over the support extended to the militants by the local populace.