The death of Golestan brings the number of journalists killed in Iraq since the conflict began to four.
Channel 4 journalist Gaby Rado fell to his death from a hotel roof in the northern Iraqi town of Sulaymaniyah at the weekend, after ITN's Terry Lloyd died near Basra and Australian Paul Moran, an Australian Broadcasting Corporation cameraman, was killed by a car bomb explosion near the camp of the northern Iraq-based Kurdish militant group Ansar al-Islam, which is linked to Al-Qaeda.
Golestan was killed as he and his colleagues, which included correspondent Jim Muir and a local translator who were both unhurt, were driving towards the town of Kifri in the southern part of the Kurdish area of Iraq on a filming trip.
According to a BBC report, Golestan got out of the car, stepped on to the landmine and was killed instantly.
The Iranian-born Golestan, 52, had worked for the BBC in a freelance capacity for about three years and was the BBC's contract cameraman in Tehran.
Golestan was acclaimed for his work during the Iranian Revolution and the gassing of the Kurds by Saddam Hussein in 1988 during the Iran-Iraq War.
He leaves a wife and an 19-year-old son.
The BBC said Hughes, 31, who injured his foot, was taken by ambulance to the American Military Hospital in Sulaymaniyah for treatment.
BBC director of news, Richard Sambrook, said: "Kaveh Golestan was an outstanding photojournalist who had worked in support of freedom of expression in his native Iran and elsewhere, and was well known to many western news organisations.
"He had worked with the BBC for many years. Our deepest sympathy goes to his family and friends. This once again underlines the dangers faced by news teams covering the war in Iraq."
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