Kuwait's government has been locked in a battle with parliament for months, delaying key legislation in the world's seventh largest oil exporter.
Earlier on Monday, 10 MPs scheduled a no-confidence vote against Sheikh Ali, who is a member of the ruling family, for July 9.
"With the resignation of the oil minister there will be no special session for the no-confidence vote on July 9 and the session will be used to discuss budgets of state organisations," Kharafi said.
The row over Sheikh Ali erupted after the minister told al-Qabas newspaper that he had sought advice from Sheikh Ali al-Khalifa al-Sabah, a former minister who was once investigated over a corruption scandal.
The minister had apologised to parliament but reiterated he had not allowed anyone to influence Kuwait's oil policy.
It was not immediately clear why Moasherji had stepped down
Kuwait's parliament has a history of challenging the government, but Emir Sheikh Sabah al-Ahmad al-Sabah, the country's ruler, has urged MPs to let the government get on with its work.
Kuwait's rulers have dissolved parliament several times since it was set up in 1963.