The collapse late on Saturday next to where Jewish women pray at the site commonly known as the "wailing wall" sent people fleeing from tumbling rocks.
The Muslim authority for the area, the Waqf, blamed Israeli building work nearby for the problem; but an Israeli architect said construction by Arabs was making the wall unstable.
"It is a miracle nobody was hurt," said rabbi Shmuel Rabinovich on Sunday, blaming time and the weather for the collapse.
Engineers were also looking at whether a small earthquake last week might have played a part in the incident. Israeli police kept people away from the site on Sunday.
The head of the Waqf, whose authority includes the al-Aqsa mosque above the wall, said it had been complaining about Israeli renovations of the Western Wall plaza for some time.
"We have been saying it could cause problems," said Adnan
Israeli archaeologist Eilat Mazar said it was the fifth time in two years that parts of the walls had begun to crumble, buckle or crack as a result of what she called unsupervised construction by the Waqf - a charge the Muslim clerics deny.
"What concerns me most is the Temple Mount itself is in danger of collapsing...The earthquake has certainly done more damage but nobody goes to check," she told Reuters.
Jewish women worship separately from men and Rabinovich said partitions would be set up in the men's section to allow women to pray there until their area was made safe after the collapse.
New Yorker Frady Schwartz, praying at the wall on Sunday, was unfazed; she said with a shrug: "It is in God's hands."
The Middle East snowstorm left a total of three dead in Lebanon and Jordan, where many called the weather a blessing for their water-starved country.
Many Jordanians saw the weather
as a blessing for their country
Strong winds buffeted Jordan overnight and snow fell heavily on northern and central regions of the country including the capital Amman, trapping motorists, causing flight delays and closing schools and banks.
Snow showers also hit the southern governorate of Tafileh, where two people were killed when their car overturned, probably after skidding on icy ground, Petra news agency reported.
Civil defence officials quoted by the agency said they had
carried out 367 rescue missions linked to the bad weather since midday on Saturday, rushing pregnant women to hospital and assisting stranded motorists.
Villages cut off
In Lebanon, hundreds of villages remained cut off by snow-choked roads and an elderly resident of Chtaura, east of Beirut, was electrocuted by a fallen high-voltage wire, police said.
Major roads were blocked, including the route between Beirut and the Syrian capital Damascus, and maritime traffic in the Lebanese ports of Sidon and Tyre in the south was halted.
Snowfall that began on Friday across Syria closed most of the
mountain roads around Damascus, weather services reported.
In the central-western region of Homs, heavy rains forced road closures, while the newspaper al-Baath said they heralded "an excellent farm season".