Police spokeswoman Luba Samri said Hadas Malka, 23, was responding to an attack nearby when a Palestinian assaulted her with a knife. One of the terrorists held a Carl Gustav M/45 submachine gun and luckily, the gun jammed, which prevented a much more serious incident from occurring.
The wounded Israeli soldier is undergoing emergency surgery at the Hadassah Hospital Mount Scopus, doctors told local reporters.
Tens of thousands of Palestinians from the occupied West Bank were given permits by Israeli authorities to enter occupied East Jerusalem on Friday for Ramadan prayers.
Israeli police said the three Palestinian assailants were killed.
Large numbers of heavily armed security forces were patrolling throughout the Old City, an AFP reporter said.
Palestinian security forces identified the Palestinians as Bara' Saleh and Adel Ankoush, both 18 and from Deir Abu Mashal near Ramallah, and 31-year-old Amer Badawi from Hebron.
Israel says that over 160 Palestinians have been killed while attempting to stab, shoot or ram Jewish citizens with vehicles since 2015, in a waxing and waning standoff that has become known as the Stabbing Intifada.
Since October 2015, Palestinian assailants have killed 42 Israelis, two visiting Americans and a British student, mainly in stabbing, shooting and vehicular attacks.
Halevi said that in the wake of the attacks, the police will consider re-imposing some of the restrictions that were lifted to allow more Muslims from the West Bank and Gaza to arrive for prays in Jerusalem during the holy month of the Ramadan.
The Old City in annexed east Jerusalem is one of the focal points of the wave of violence.