The shootout in the city of Salt, northwest of the capital Amman, came after a home-made bomb exploded Friday under a patrol car at a music festival killing one security force member and wounding six others.
The rare blast hit the security patrol in Al-Fuhais, 12 kilometres (8 miles) west of the capital on Friday evening, the interior ministry said on Saturday.
"It killed Sergeant Ali Adnan Qawqaza and wounded six other members of the patrol," the ministry said, adding that an investigation was underway into the cause of the blast.
Security forces had been deployed to protect the town's annual festival, which hosts prominent Arab music acts.
Later Saturday, security forces raided a house in Salt in search of a suspected "terrorist cell" believed to be behind Friday's bombing, government spokeswoman Jumana Ghneimat said in a statement.
"The suspects refused to surrender and opened heavy fire toward a joint security force," Ghneimat said.
The suspects also "blew up the building in which they were hiding, and which they had booby-trapped earlier", she said, adding that part of the building "collapsed" during the raid.
Three members of the security forces were killed in the shootout and several others, including civilians, were wounded, said Ghneimat, who is also minister of state for media affairs.
Ghneimat did not give details but local Jordanian media, quoting medical sources in Salt, said around 20 people were wounded in the operation.
The security forces eventually arrested three suspects, she said, adding that the operation in Salt was still "ongoing".