Manoj Sinha, the district's chief magistrate, wrote on
Officials said the bus was heading to the base camp of Mata Vaishno Devi, a famous Hindu temple, when it came under fire.
No one has claimed responsibility for the attack, but local police chief Mohita Sharma told Reuters that suspected militants had ambushed the bus.
The Himalayan region of Kashmir has been a flashpoint between India and Pakistan for more than 60 years.
Since 1947, the nuclear-armed neighbors have fought two wars over Muslim-majority territory. Both claim the whole but are in partial control. Since 1989, an armed rebellion against Delhi's rule has taken place in Indian-administered Kashmir, killing thousands of people.
Delhi accuses Islamabad of harboring militants and disrupting regional peace, a charge Pakistan denies.
News of Sunday's attack broke as Prime Minister Modi was sworn in to become India's prime minister for a third consecutive term at an inauguration ceremony in Delhi.
The passengers' identities have not yet been confirmed but they are believed to be from the northern Indian state of Uttar Pradesh, Ms Sharma told the newspaper.
Photos showed some of the injured, including women, being taken to a hospital in Jammu for treatment.
