"UNICEF estimates that most water pumping will gradually cease across the country in the next four to six weeks," a statement by the UN body said.
Lebanon is battling an economic meltdown that has propelled more than half of its population into poverty and seen its currency lose over 90% of its value in less than two years.
The financial crisis has translated into severe shortages of basic goods such as fuel and medicine as dollars run dry.
UNICEF said that should the public water supply system collapse, water costs could jump by 200% a month as water would be secured from private water suppliers.
The UN agency said it needed $40 million a year to secure the minimum levels of fuel, chlorine, spare parts and maintenance required to keep critical systems operational.
"Unless urgent action is taken, hospitals, schools and essential public facilities will be unable to function," UNICEF Representative in Lebanon, Yukie Mokuo, was quoted as saying in the statement.