Gulab Chand Kataria, the Rajasthan state home minister, said: "We have detained around one dozen people and we are trying our best to unravel the conspiracy behind this dastardly attack."
A rickshaw puller and one of the 200 wounded were among those arrested, a police official added.
Police say the bombs, many of them strapped to bicycles, exploded within minutes of each other on Tuesday evening.
The blasts targeted busy markets and Hindu temples, leaving hundreds of people injured.
"The way it has been done, the attempt was to cause the maximum damage to human life"
Rajasthan state police chief
No one has claimed responsibility for India's deadliest bomb attacks in nearly two years.
Authorities have suggested Pakistan-based groups, which India accuses its neighbour and rival of backing, were to blame.
"Obviously it's a terrorist attack," said A.S. Gill, the police chief of Rajasthan.
"The way it has been done, the attempt was to cause the maximum damage to human life."
An eighth bomb failed to explode and was defused by police.
Al Jazeera correspondent Matt McClure, who is in Jaipur, said building and shop signs around one of the attack sites were pockmarked with holes from ballbearings that police say were packed into the bombs.
'State of terror'
Ashok Parnami, the city's mayor, said Jaipur had been placed in "a state of terror" by the attacks.
|The series of blasts targeted busy |
areas of Jaipur's old walled city [EPA]
One bomb went off at a market near a temple dedicated to the Hindu monkey god Hanuman.
Tuesday is the day of worship set aside for Hanuman, and the temple was crowded with people offering prayers on their way home from work.
Another bomb detonated near the Johari Bazaar, the city's jewellery market and a popular tourist destination.
May is considered low season for the city's tourism industry and there were no immediate indication that foreigners had been caught in any of the explosions.
"One can't rule out the involvement of a foreign power," said Sriprakash Jaiswal, India's junior home minister. He refused to say if he was talking about Pakistan, but said "the blasts are part of a big conspiracy".
Spate of bombings
Pranab Mukherjee, India's foreign minister, is due to visit Pakistan in just over a week to review the four-year-old peace process.
His trip will be his first since a new, civilian government took over in Pakistan.
Indian authorities have blamed Pakistan-based groups for a spate of bombings that have killed nearly 400 people since 2005.
Pakistan denies any role in the bombings.
Indian authorities stepped up security at airports and railway stations across the country after Tuesday's attacks.