The blasts occurred shortly after hundreds of worshippers had offered the late afternoon prayers at the crowded 17th-century Jama Masjid on Friday.
KK Paul, the police commissioner, said: "There was an explosion at 5:20pm (1150 GMT). After seven to eight minutes there was another small explosion.
"It was a low-intensity improvised device," he said, adding that 10 people were injured.
The NDTV television channel said police believed explosives were placed in plastic bags, with no evidence of a timer.
Sayeed Ahmed Bukhari, the mosque's imam, said: "I saw one man critically injured and women running with their bleeding children on their arms."
"We did not see the first explosion but the second one definitely originated from a bag that was kept inside the prayer grounds," the imam said.
Police initially barricaded the area and searched for more explosives, but worshippers were allowed back into the mosque for evening prayers less than an hour and a half after the blast.
The mosque, built by Mughal Emperor Shah Jahan in the 17th century, is the largest in India and is located in the old, crowded part of the city near the historic Red Fort.
It was not damaged by the blast.
In October, three powerful bombs ripped through packed markets in New Delhi before the biggest Hindu and Muslim festivals, killing at least 66 people and wounding more than 100.
The blasts occurred just after
the late afternoon prayers
On Tuesday, in neighbouring Pakistan, a suicide bomber killed 57 people at a congregation of more than 15,000 Sunni Muslims, Pakistan's majority sect, celebrating the birth anniversary of the Prophet Muhammad at a city park.
Sporadic trouble erupted in Karachi on Friday and traders kept businesses shut after Sunni Muslim groups called for a strike to protest against the killing.
Indian police arrested six men on April 4 linked to triple bombings that killed more than 20 people in the holy Hindu city of Varanasi last month.
The explosions went off almost simultaneously on March 7 at an ancient temple packed with devotees and a crowded railway station, killing 23 people and injuring 68 in Varanasi, India's most important Hindu pilgrimage city.