Ten Kuwaiti parliament members presented the motion last month against Sheikh Ahmad al-Abdullah al-Sabah, who is also acting information minister, over alleged financial and administrative breaches at the health ministry.
The vote was set to take place in parliament on Monday and Sheikh Ahmad would have had to step down if MPs had voted against him. The cabinet's resignation automatically cancels the parliament session.
''I have been informed that the government has presented its resignation,'' parliament member De'ij al-Shammari told Reuters.
Sheikh Ahmad had refused to resign, resulting in a stand-off between the elected parliament and the government of the oil producer, where the emir has the last word in politics.
The emir, Sheikh Sabah al-Ahmad al-Sabah, must now either appoint a new prime minister to form a government or ask existing Prime Minister Sheikh Nasser al-Mohammad al-Sabah to find a new line-up.
Parliament members expect him to keep Sheikh Nasser on.
The emir had the option of dissolving parliament to avoid the vote, but political sources had said that was unlikely because, though he has dissolved parliament before, it would have caused a constitutional crisis.
The emir dissolved parliament last year after a stand-off between the government and opposition over reforms.
Kuwait's parliament has a history of challenging the cabinet, whose prime minister must be from the ruling family, in a region where the public plays little role in political change.
In December, Information Minister Mohammad al-Sanousi resigned a day ahead of an expected grilling by an Islamist MP, but it is far more sensitive for a member of the ruling family to be removed by an elected body.
Sheikh Ahmad was named acting information minister after Sanousi's resignation. He said in parliament last month that mistakes had been made in his ministry.
REUTERS SHB RN1732