The first attack occurred outside a local restaurant and minutes later an explosives-packed car rammed a security checkpoint in the same area, officials said.
"The toll has now reached 50 dead and 87 wounded," Abdel Hussein al-Jabri, deputy health chief for the mainly Shiite province, told reporters.
Officials fear that the final death toll could rise, as many of those injured in the attacks are in serious critical condition.
According to security officials, the attackers were disguised as members of the Hashed al-Shaabi Shiite paramilitary units that have joined the government forces in their fight against Daesh terrorists to the north of the capital Baghdad.
Jihadist militants carry out regular attacks in Iraq where Daesh has been losing ground to the government forces.