Her coffin almost fell as police, some using batons, waded into a crowd of Palestinians gathered around it.
Police said they acted after being pelted with stones.
Abu Aqla was shot dead in disputed circumstances on Wednesday, with Israel and Palestinians trading blame. The killing has been widely condemned.
Footage showed a standoff between police and Palestinians gathered around the coffin in the hospital compound, before officers push the crowd back, with some beating and kicking mourners. Police said officers "were forced to use riot dispersal means".
A spokesman for UN Secretary General Antonio Guterres said he was "deeply disturbed" by the confrontations between Israeli security forces and Palestinians and the behaviour of some police.
White House spokeswoman Jen Psaki also said the images of police hitting mourners were disturbing.
"We regret the intrusion into what should have been a peaceful procession," she said.
The Palestinian Authority and Al Jazeera claim Abu Aqla was shot dead by Israeli forces, while Israel said it was not yet possible to determine what happened and that she could have been killed by Palestinian gunfire.
An Israeli military interim report on Thursday said the fatal shot could have come from "massive fire from Palestinian gunmen", or possibly from "a few bullets" fired by a soldier "at a terrorist who was firing at his vehicle".
Shireen Abu Aqla was known to millions for her coverage of the Israel-Palestinian conflict
Shireen Abu Aqla, a 51-year-old Palestinian American, was a veteran correspondent for Al Jazeera's Arabic news channel and had reported on the Israel-Palestinian conflict for two decades.
She was given the rarity of a funeral at the compound of Palestinian President Mahmoud Abbas on Thursday, where her coffin was brought draped in the Palestinian flag. President Abbas paid tribute to her, describing her as a "martyr of the free word" who "sacrificed her life" to defend the Palestinian cause.
He said Israel was "fully responsible for her killing" and that he would refer the case to the International Criminal Court, which investigates potential war crimes.
Israeli Prime Minister Naftali Bennett has accused Mr Abbas of "throwing blame at Israel without any basis".
Abu Aqla was in the Jenin refugee camp early on Wednesday to report on the Israeli raid. The Israeli military said the operation was to apprehend "terrorist suspects".
It said: "Tens of Palestinian gunmen fired at and hurled explosive devices toward the soldiers. The soldiers responded with fire toward the gunmen and hits were identified."
Another Palestinian journalist, Al Jazeera producer Ali Samoudi, was shot and wounded during the violence.
The incident comes at a time of particularly high tension between Israel and the Palestinians, after nearly two months of one of the deadliest periods of violence in years. Israel has carried out operations in Jenin in the wake of a wave of killings of Israeli Jews by Palestinians and Israeli Arabs in Israel and the West Bank.
Seventeen Israelis and two Ukrainians have been killed in stabbings, shootings, car rammings and an axe attack. In the same period, dozens of Palestinians have been killed - including assailants shot dead while carrying out attacks, or militants and civilians killed during Israeli raids and confrontations.
Four of the Palestinians who carried out attacks in Israel came from the Jenin district.
An Israeli police commando meanwhile was killed on Friday during clashes with Palestinian gunmen near Jenin, police said. The commando, who was 47, was shot dead during an operation to arrest a suspect, Israeli authorities said.
-- Courtesy of BBC Sport