One of the bombs went off near a Hindu temple, leaving blood splattered on the streets and cycles and rickshaws in a mangled heap, television showed.
“Sixty people have died and 150 are injured,” Vasundhara Raje, the chief minister of the western desert state of Rajasthan told reporters.
At least seven bombs exploded, most within a few minutes of each other, killing at least 60 people and injuring around 150, police, officials and witnesses said.
The bombs all exploded in Jaipur's crowded walled city, an area often frequented by tourists. One was beside a Hindu temple.
Police said they had confirmed more than 20 deaths, but a Reuters reporter said he had seen at least 25 bodies at the main hospital in the city. The NDTV news channel said 35 people had been killed.
India's Junior Home Minister Shri Prakash Jaiswal told local television that the blasts were caused by bombs and said 100 people had been injured.
'I heard a deafening noise and I thought it was a (gas) cylinder blast,' witness Hemanth Modi told the NDTV news channel. 'There was smoke and I could not find my son. Then I found him.'
Television stations showed images of wrecked bicycles and pools of blood, with sirens blaring in the background. They said the blasts had caused panic in the narrow streets.
'People started running around and I followed them,' Anil Garg told NDTV. 'There are huge traffic jams. I am very scared.'
Alerts were also issued in the Indian capital New Delhi and the country's financial capital Mumbai.
'We'll be on high alert,' said sub-inspector Shivaji Vishnu Patil in the Mumbai police control room. Although police are not aware of any specific threat in Mumbai, he said extra armed police would be sent to power stations, prominent mosques and Hindu temples and other potential targets as a normal precaution.
In the past few years a string of bomb blasts in Indian cities have killed hundreds of people. The most deadly was an attack on Mumbai's railway system in July 2006, when seven explosions killed more than 180 people.
In August last year, three bombs killed 38 people inside an amusement park and at a street-side food stall in Hyderabad, a city in southern India which is home to a booming outsourcing industry.
In November, nearly simultaneous explosions in three northern Indian cities -- Varanasi, Lucknow and Faizabad -- killed at least 13 people.
Cinemas, markets and places of worship have also been targeted in recent years.