Micky Rosenfeld said the 49-year-old woman from east Jerusalem had tried to stab forces near Damascus Gate.
Initially, police said she was armed with a knife but later said she was using scissors.
Police released images purported to show the woman, wearing a black Islamic headscarf and robe and holding a sharp object in a threating way.
Local media said that he woman's son was shot and killed last year in an apparent mistake by the police.
Since then, Palestinians have killed 41 Israelis and two visiting Americans, mainly in stabbing, shootings and assaults using cars.
Israeli forces have killed at least 240 Palestinians during the same period. Most of the slain Palestinians have been identified as attackers by Israeli authorities.
Israel says the violence is fueled by a Palestinian campaign of incitement. Palestinians say it stems from anger over Israeli rule in territory they claim for a state.
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