The incident occurred hours before US Vice President Joe Biden was due to arrive for talks with Israeli Prime Minister Benjamin Netanyahu and Palestinian president Mahmud Abbas.
Israeli police said the woman moved toward border police officers, pulled a knife from her bag and sought to stab them near Damascus Gate, the main entrance used by Palestinians to enter the walled Old City where several attacks have occurred.
The woman was said to be around 50 years old and from Israeli-annexed east Jerusalem, where Damascus Gate is also located.
Most of the Palestinians who died in the violence were killed while carrying out knife, gun or car-ramming attacks, according to Israeli authorities.
Others were shot dead by Israeli forces during clashes or demonstrations.
The number of attacks has diminished recently, but increased Israeli security has failed to stop them entirely.
Many analysts say Palestinian frustration with Israeli occupation and settlement building in the West Bank, the complete lack of progress in peace efforts and their own fractured leadership have fed the unrest.
