Huge protests have nonetheless demanded Rajapaksa stand down, including tens of thousands of people camped outside his seafront office for more than a week.
The new cabinet retains prime minister Mahinda Rajapaksa, Gotabaya's older brother and the head of Sri Lanka's ruling clan, while leaving out eldest sibling Chamal and younger brother Basil, the former finance minister.
Mahinda's eldest son Namal, who ran the sports ministry and had been touted as a future leader before the crisis, was also dropped.
The 21-member cabinet is seven people fewer than its predecessor, which resigned en masse two weeks ago in response to public outrage over nepotism and corruption.
Ministers are entitled to several SUVs, a large contingent of bodyguards and unlimited fuel, as well as state housing and entertainment allowances.
New finance minister Ali Sabry led a delegation to Washington over the weekend to open talks with the International Monetary Fund from Tuesday, officials said.
Sri Lanka is seeking three to four billion dollars from the IMF to overcome its balance-of-payments crisis and boost depleted reserves.
Apart from the acute shortages, the country is also facing record inflation and lengthy electricity blackouts, as the government has run out of foreign currency to import fuel.
The government last week announced a default on Sri Lanka's $51 billion foreign debt and the Colombo Stock Exchange has suspended trading for the week to prevent an anticipated market collapse.
Rajapaksa's parliamentary majority has been thrown into question after former allies deserted the ruling coalition.
The opposition has said it will attempt to topple the government through a no-confidence vote in the coming weeks.