Preliminary information indicates that "direct damage" from floods was greatest in the housing, roads, irrigation and agriculture sectors, the bank said.
Large parts of the flood-hit areas are still cut off by floodwaters that have washed away roads and bridges.
"We have been told that for the past two weeks people here have not received any help. They are running out of food and they are running out of medicine," Al Jazeera’s Kamal Hyder reported from Dubair in northern Pakistan.
Al Jazeera's Imran Khan, reporting from Shikarpur in the southern Sindh province, witnessed how hundreds of people, living in make-shift homes, were still waiting for food aid.
"There is no visible government presence in this part of the country, no international aid groups are operating here, yet.
"These people are going to be living in these conditions for months to come. The floodwaters [...] are not receding any time soon. And when they do, the true devastation of this disaster will be revealed," he said.
Islamabad last week asked the World Bank, the Asian Development Bank (ADB) and the United Nations to carry out assessments in the flood-hit areas in relation to damages, needs and recovery initiatives.
The two banks and the UN "will collaborate through participation and sharing of information on their respective assessments, and will also regularly co-ordinate with key donors," the World Bank said.
A "global facility for disaster reduction and recovery rapid response team" arrived in Islamabad, the capital of Pakistan, on Friday to help launch the assessment.
"If there is no fresh wave of flooding, the assessment can be completed by October 15," the World Bank said.
Pakistan won more aid pledges on Tuesday amid concerns that money is not coming through fast enough.
The United Nations last week launched an immediate appeal for $460 million to cover the next 90 days and UN chief Ban Ki-moon visited Pakistan at the weekend, calling on the world to quicken its aid pledges.
Officials now estimate that 35 per cent of the funds have been committed.
State media in Saudi Arabia on Tuesday said the country had raised $20.5 million in aid on the first day of a national campaign for the Pakistani floods.
Japan also came forward to pledge an additional $10 million in emergency aid and Australia promised an extra $21.6 million.
"There are grave risks that the flooding will worsen Pakistan's social circumstances, but also its long-term economic circumstances will be potentially devastating," Stephen Smith, Australia's foreign minister, told ABC Radio.
The cost of rebuilding Pakistan could exceed $10 to $15 billion, the country's high commissioner to Britain said on Monday.
"It will take at least five years," High Commissioner Wajid Shamsul Hasan told the Reuters news agency.
He said the figures are a rough estimate because an assessment of the extent of the damage caused by the floods had yet to be carried out.
But the number gave an indication of the scale of the reconstruction needed.
"These floods have really dislocated everything," Hasan said.
"In the longer term, when the water subsides, we need reconstruction ... We'll have to have a long-term plan, something like the Marshall Plan."
With more than 20 million people made homeless by the floods, authorities have been overwhelmed by the scale of the disaster, and many people have been angered by the lack of assistance they have received.