The incident occurred after clashes broke out between Jewish settlers and a number of local Palestinians in the Silwan neighbourhood, Al Jazeera's Dan Nolan reported from Jerusalem on Wednesday.
Israeli policemen fired rubber-coated bullets and teargas at stone-throwing Palestinian protesters after the shooting, leaving several Palestinians wounded.
"Early this morning a private security guard drove in his car when the road was blocked with garbage. Cans and stones were throne at him from an upper level by tens of people," Mickey Rosenfeld, an Israeli police spokesman, said.
"The security guard pulled his gun and shot dead a 32 year-old local citizen. The man who was killed is known to the police. His body was taken for examination. The security guard was arrested. The investigation is still in process," he said.
Silwan, a crowded Arab neighbourhood of roughly 45,000 Arabs, is one of the most volatile areas of East Jerusalem, which Israel occupied in 1967 and later annexed in a move not recognised by the international community.
Plans to demolish Palestinian homes to make way for an archaeological park have triggered violent protests in the past.
The Jerusalem city council gave the green light in June for the controversial project which would be under the control of Elad, a group dedicated to expanding Jewish ownership in east Jerusalem.
Under the plan, 22 homes would be razed, while another 66 would be legalised.
The park is planned on what is believed to be the site of ancient Jerusalem during the reigns of the biblical kings David and Solomon.
Wednesday's shooting highlighted the challenges Israeli and Palestinian negotiators face in peace talks which resumed on September 2 after a 20-month hiatus.
The issue of settlements has been one of the thorniest in peace efforts.
The international community considers Israeli settlements in the West Bank, including East Jerusalem, to be illegal.
The Palestinians want a freeze on all settlement construction but are also pushing for a renewal of a partial moratorium on settlement building that will end within days, even though the curbs do not cover east Jerusalem.
The Israeli government does not consider Jewish residents of East Jerusalem to be settlers as it views the whole of the Holy City as its "eternal and indivisible capital".
Source: Al Jazeera