The Colombo Municipal Council will not go to the polls as scheduled in March while four other councils in the central and southern provinces will also be delayed to avoid clashing with the tournament.
"There will be no elections in these areas while World Cup matches will be played," an information department official said. Sri Lanka will host 12 matches in Colombo, Kandy and Hambantota. India and Bangladesh are the other hosts of the World Cup, which starts on February 19.
The polls will be the first set of nationwide local elections since the crushing of Tamil Tiger rebels in 2009 and is a key test for the government of President Mahinda Rajapakse.
The president tightened his grip on power by winning a second term in 2010 and winning parliamentary polls in April by a landslide. New dates of the delayed polls have not been announced.