The girl, who was playing outside her house in Shastri Nagar neighbourhood, was picked up by a man on a motorcycle who said he needed to give her father some money.
When the family realised the girl was missing, they raised an alarm.
The seven-year-old was found two hours later near the Amanishah canal that runs through the city, about 15 kilometres away.
The girl is now being treated at a hospital in Jaipur and her condition is stable.
"The man beat her with a belt, there are also stitches on her forehead. He left her where we found her - about ten to fifteen kilometres from home," said a family member.
People in the area stormed the local police station demanding action. Some went on a rampage smashing vehicles and car windows.
The police had to deploy extra forces and 16 people have been taken into custody for the violence.
On Tuesday evening, after a meeting with community leaders, police says the situation is now under control though internet has been suspended in areas under 13 police stations in and around Shashtri Nagar, especially the sensitive Ramganj area.
"People spreading rumours on social media will be dealt with very strictly. The child is undergoing treatment and her condition is stable. We have formed 14 police teams to catch the culprit," said Jaipur Police Commissioner Anand Srivastava.
People in the area say the reason for the anger is that just 10 days ago a similar incident took place when a four-year-old girl was picked up from outside her house in a similar manner and was raped.
Despite the family registering an FIR, the culprit - who people believe could be the same as the one in the case of the seven year old girl - was never traced.
The police have prepared a sketch of the accused based on the child's description and have formed 14 teams to search for him.