The missiles struck locations in Pakistan-administered Kashmir and in the country's eastern Punjab province, according to officials.
One of them struck a mosque in the city of Bahawalpur in Punjab, where a child was killed and a woman and man were injured, one official said.
India says it has attacked "terrorist infrastructure" in nine sites and Pakistani authorities vowed to respond to the attacks.
After the strikes, the Indian army said in a post on X: "Justice is served."
India's offensive occurred amid heightened tensions in the aftermath of an attack on Hindu tourists in Indian Kashmir last month. Islamist assailants killed 26 men in the April 22 attack, the worst such violence targeted at civilians in India in nearly two decades.
Pakistan said India launched missiles at three places, but an Indian government statement did not detail the nature of the strikes.
Indian TV channels showed video of explosions, fire, large plumes of smoke in the night sky and people fleeing in several places in Pakistan and Pakistani Kashmir. Reuters could not independently verify the footage.
Witnesses and one police officer at two sites on the frontier in Indian Kashmir said they heard loud explosions and intense artillery shelling as well as jets in the air.
Pakistani Prime Minister Shehbaz Sharif said Islamabad was responding to the Indian attacks but did not provide details.
An emergency was declared in Pakistan's populous province of Punjab, its chief minister said, and hospitals and emergency services were on high alert.
"A little while ago, the Indian armed forces launched 'OPERATION SINDOOR', hitting terrorist infrastructure in Pakistan and Pakistan-occupied Jammu and Kashmir from where terrorist attacks against India have been planned and directed," the Indian statement said.
"Our actions have been focused, measured and non-escalatory in nature. No Pakistani military facilities have been targeted. India has demonstrated considerable restraint in selection of targets and method of execution," it said.
Speaking to reporters at the White House, US President Donald Trump called the situation "a shame" and added,:"I hope it ends quickly."
Trump said he had just heard about the intensification of hostilities that had occurred in recent hours.
The name of India's military operation, Sindoor, is an apparent reference to the women who lost their spouses in the attack on Hindu tourists in Pahalgam last month.
Sindoor is the Hindi for the traditional red vermilion worn by married Hindu women on their forehead symbolising protection and marital commitment. Women traditionally stop wearing it when they are widowed.
with AP
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