Fukuda, who abruptly resigned two weeks ago, will formally stay in office as Japan's prime minister until parliament appoints the next prime minister following the September 22 vote of the ruling Liberal Democratic Party.
On Tuesday, Wickremanayake will attend the opening ceremony of the Sri Lanka Cultural Heritage Exhibition in Tokyo, before meeting Fukuda on Wednesday afternoon, a foreign ministry official said.
"The primary purpose of his visit here is to attend the opening ceremony of the exhibition" which the Sri Lankan government co-organised with a Japanese newspaper company, the official said.
Tens of thousands of people have died in Sri Lanka in more than three decades of bloodshed since Tamil Tiger rebels launched a campaign to carve out an independent homeland for minority Tamils in the majority Sinhalese nation.
Tokyo has sent its special envoy to the country four times in the past three years to help build a peace deal with the rebels and Japan provides nearly two-thirds of