One of the suspected assailants was also killed and about 20 people were injured. It is the second attack against a Christian target in Pakistan in less than a week.
The incident happened on the grounds of the Western-financed hospital in the ancient Buddhist town of Taxila, about 40 kilometres (25 miles) north-west of Islamabad.
"The nurses were coming out of the chapel when someone threw explosives," Clement Bakhshi, an accounts officer at the hospital, told Reuters news agency.
The attack follows a spate of violence against Christian and Western groups in the country, and comes just four days after six Pakistanis were shot dead at a missionary school for foreigners in the town of Murree, also near Islamabad.
BBC Islambadad correspondent Zaffar Abbas says the authorities believe the attacks are linked, and are the work of Islamic extremists who oppose Pakistan's support for the US-led war on terror.
Information Minister Nisar Memon said such attacks strengthened the government's resolve to defeat those behind them.
"These are not human beings. They are animals, savages," he told the BBC.
"They are going to fail terribly, miserably."
Deadly explosions
Witnesses to the chapel attack said they heard two explosions.
"We saw many women fall down," said Slomy Cissel, 28, who was hit by shrapnel as she came out of the church.
Pakistan attacks:
"Window-panes were falling on us, everyone was crying, everyone was in pain," said another worshipper, Margif Tariq.
The three dead and most of the wounded were Pakistani women. Local custom dictates that women leave social gatherings before men and children.
Many of injured were taken to a hospital in the nearby town of Wah, some in a serious condition.
A post-mortem is being conducted on the body of the dead attacker. Police say a small hole in his back suggests he may have been hit by a fragment from his own grenade.
Shahbaz Bhatti, who heads the All Pakistan Minorities Alliance, said the country's Christians were paying the price of being allied with the West.
"I think now it will be a complete genocide of the non-Muslims here if the Islamic militant forces are not checked."
Security fears
The missionary hospital attack is the latest in a string of violent incidents directed at foreign targets in Pakistan.
Security fears have prompted Australia's cricket team to announce it is pulling out of a three-Test tour of the country.
The Italian consulate in Karachi has also closed its visa section after a security alert - the third consulate to halt operations in the city in less than a month.
On Thursday, the body of US journalist Daniel Pearl, abducted in January and murdered, was flown back to America.
Police say the three gunmen who attacked Murree Christian School on Monday blew themselves up a day later after escaping from a police checkpoint in Pakistan-controlled Kashmir.
Before killing themselves, they apparently warned that other groups are planning similar attacks on Americans.