Political sources said several other legislators from the president's Sri Lanka Podujana Peremuna (SLPP) party had declined to take up portfolios.
"There is tension between the SLPP and others in the unity government," a government official involved in the cabinet formation told AFP. "At least four MPs have refused to take up ministries."
Wickremesinghe took over earlier this month after Mahinda Rajapaksa, the president's elder brother, resigned after months of anti-government protests turned violent, with at least nine people killed.
Wickremesinghe, 73, had pledged to put together a cross-party coalition after the previous cabinet was dissolved.
The new ministers -- for fisheries, agriculture, transport, environment, culture and irrigation -- were sworn in before the president at his tightly-guarded official residence in Colombo.
The delay in getting a finance minister could hinder the IMF negotiations about a bailout, the central bank chief warned on Thursday.
The country of 22 million people has been enduring severe economic hardships for months.
Consumers have been unable to access petrol, diesel and cooking gas, while staple food has been rationed. The country is also facing record inflation and lengthy daily electricity blackouts.
Last month, Sri Lanka announced it would default on its $51 billion external loans as the country ran out of dollars.