Additional Director General of Police (Headquarters) Gupteshwar Pandey told PTI that the explosion took place around 11.30 am when a van carrying undertrials for production in the court entered the premises and they were being taken to the court lock-up.
The woman, suspected to be carrying the explosive, was aged about 35-40 years, the ADG said adding that there was a possibility that she could be a human bomb.
Bomb splinters have been found on her body and a mobile recovered from her person. A police constable Amit Kumar, 40, was the other person killed, he said.
Pandey, however, ruled out the possibility of the blast being a terror attack.
Bihar Chief Secretary Anjani Kumar Singh said in Patna that the Ara blast appeared to be aimed at helping undertrials flee.
The two undertrials who managed to flee included Lambu Sharma, who had made a similar attempt at the Ara court premises in 2009 when his gang men exploded bombs.
Ara Superintendent of Police Akhtar Hussain said that in addition to Lambu Sharma another undertrial Akhilesh Upadhaya also fled taking advantage of the explosion.
Ara MP R K Singh also told reporters on the sidelines of a BJP function in Patna that prima facie the blast appeared to be part of design to help the under-trials flee.
"As per my information two under-trials have escaped taking advantage of the commotion after the explosion," he said.
Bhojpur District Magistrate Pankaj Kumar Pal said about 16 people, including 3 lawyers and as many policemen, were injured and taken to the civil hospital.
The ADG said the district administration has sealed the court premises.
Lawyers and eyewitnesses said the woman was sitting between the van, which was parked near the gate and the court lock-up about 8-10 feet away.
As the undertrials were being taken from the van to the lock-up one by one, the bomb exploded, they said.
Five policemen have been suspended following recovery of some mobile phones, SIM cards and food items in the lock up at Patna civil court, he said.
Those suspended policemen were four of sub inspector rank and a constable, Rana added.