Mine-clearing operations are taking place so residents can return after Iraqi forces backed by US-led coaltion air strikes recaptured the city from Islamic State in December.
The Foreign Office said it had spoken with officials at Janus, a US contractor following the incident. "We are in contact with the employer of a British national who has died in Iraq and have offered our support at this difficult time," said a spokesman.
The death was confirmed by the mayor of Ramadi according to AFP news agency, although he did not state the nationality of the wounded contractor.
Scored of Iraqi civilians have been killed by incendiary devices and booby-traps left by IS (Daesh) as they tried to return to their homes in Ramadi and the rebuilding of the city can start.
"Daesh did not leave a metre on the ground in the city without planting in it explosives," Ahmad Rabih, an Anbar tribal official, said in a Guardian report. "That is what slowed down our heroes. They planted them in the streets and homes and shops. You have to blow them up from afar or they will blow you up."
Janus Global Operations started working in Iraq during April after they won the contract to clear bombs and explosive devices planted around the area by Islamic militants. A spokesperson for Janus said: "Earlier today there was an incident in Ramadi at a worksite of Janus Global, the firm the [US] state department has engaged to clear that city of unexploded ordnance, abandoned explosive ordnance, and improvised explosive devices.
"The incident is under investigation, but what we can confirm is that sadly there was one fatality, a national of the United Kingdom. Another national of the United Kingdom suffered minor injuries. Until this investigation is more complete we will not be providing further information. At this point, our focus is on the family of our colleague and the health and safety of our team in the field."