Prime Minister Manmohan Singh condemned the violence and appealed for peace and calm.
The first blast came from a crude bomb that exploded in a public toilet building on an isolated railway platform, Patna district police chief Manu Maharaj said.
Another bomb went off near a movie theater, and four more exploded just outside the park, sending plumes of gray smoke swirling above the crowd.
"All the bombs produced low-intensity blasts," Maharaj said. "An anti-sabotage team is investigating what happened."
Five people died from the blasts and 73 were being treated for injuries, according to the head of Patna Medical College hospital, Vimal Karak.
Bomb disposal and forensic teams found two unexploded bombs around the railway station and were defusing them, railway police superintendent Upendra Kumar Sinha said.
Modi ignored the blasts during his speech and instead focused on criticizing Singh's government for India's high inflation. He also accused Bihar's highest elected leader, Nitish Kumar, of betraying the BJP after using its support to win his seat in the state.
After the rally, Modi said the blasts were "deeply saddening" and offered condolences and prayers to the victims, according to a message posted from his official Twitter account.
His plans to visit Bihar have been controversial since Kumar severed ties with the BJP six months ago to protest Modi's candidacy. Kumar has questioned Modi's secular credentials and suggested that he could exacerbate communal tensions between Hindus and Muslims in India.
Over the past decade, Modi has been accused of ignoring a 2002 spate of violent attacks against Muslims in his home state of Gujarat an allegation he has denied.