At least two policemen were killed in the attack that occurred late on Wednesday night while Allawi was being driven home from a meeting.
"Thank God, the prime minister is well, but some policemen and members of his security team were killed," his spokesman Thair al-Naqib said.
Reports said a bomber attempted to ram his explosive-laden vehicle into Allawi's convoy. After security guards opened fire at him, the attacker blew himself up.
The attack took place around the al-Faris al-Arabi roundabout near Zawra Park on the city's west side.
It was a massive blast and many homes in the area were badly damaged.
An interim Interior Ministry spokesman said earlier that two policemen were killed and one wounded in the attack.
The attacker's pickup truck was packed with TNT and mortar rounds, sources said.
Al-Naqib said members of Allawi's parliamentary bloc were travelling with him, but was unable to identify them or say anything about their condition.
The Interior Ministry spokesman said a suspect identified as Amir Mijbil al-Midab, an officer in Iraq's former army, was arrested near the scene of the bombing.
This was the fifth attempt on Allawi's life. Another "major plot" against the prime minister was uncovered one week ago, al-Naqib said.
Meanwhile, Aljazeera reported a tanker packed with explosives exploded near a US military position in central Ramadi.
The blast was followed by fierce shelling of mortar rounds targeting the governorate building, used as a base by US troops.
Intermittent clashes also erupted between fighters and US troops in other parts of Ramadi during the day. There were no immediate reports of casualties.