Between 45 and 60 people are believed to be dead with hundreds of others wounded, according to reports by the Associated Press and Reuters.
"According to the information I have received, 60 people have died and 150 have been injured," Rajasthan's Chief Minister Vasundhara Raje was quoted by the Press Trust of India as saying.
Bloomberg reported eight bombs exploded that were placed on bicycles around the city, in markets and near a Hindu temple. The explosions began at 7:30 p.m. and detonated within 12 minutes of each other, reported CNN.
Jaipur is a tourist destination known for its monuments from the 18th century. It is also home to the Rajasthan Royals Twenty20 cricket team, one of the highest-ranked squads in the India Premier League.
No group immediately claimed responsibility for the attacks, but India has previously blamed bombings on Islamic militants based in Pakistan who are angry over India's control of the Kashmir region.
Tuesday's attack could have been the work of extremist groups that have been crossing from Pakistan into Kashmir in recent days, reported the Telegraph. Border guards have been fighting with militants, requiring reinforcements.
"It's a terror attack. There was no (intelligence) report of this," police director general A.S. Gill told television stations, Agence France-Presse reported.
State borders were sealed after the attack and police were on high alert in major cities like Mumbai.
U.S. State Department spokesman Sean McCormack said the United States "condemns" the attacks, which he said were "quite clearly an act intended to take innocent lives."
India has been plagued by bombings over the past few years, but Tuesday's attacks were the worst the country has seen since 65 people died in a train bombing in February 2007.
In November, coordinated blasts in three cities in the Uttar Pradesh state aimed at the justice system killed at least 13 people.
