"The council (of ministers) decided to approve the draft law and transfer it to the amir (Jabir al-Ahmad al-Sabah), God protect him, in order to transfer it to the National Assembly (parliament)," the cabinet said in a statement.
The draft needs parliament's approval to pass as a law. A decree issued by the amir giving women the vote was narrowly defeated in the 50-man house in 1999, by an alliance of Islamist and conservative lawmakers.
Kuwaiti women have been fighting for suffrage for more than 40 years, only to be blocked by Islamists and male politicians.
"This challenge was not new. We had been struggling since before 1973," said Nuriya al-Saddani, writer and Kuwaiti unionist campaigning for women's rights in the Middle-East.
"Like any woman in the world, Kuwaiti women need a political voice," al-Saddani told Aljazeera.net.
She said the bill was expected to be passed quite easily.
Kuwaiti women watched in frustration when the current parliament was elected in July by an elite group of males who must be 21 years or older and not recently naturalised or members of the armed forces.
The government of Prime Minister Shaikh Sabah al-Ahmad al-Sabah, the amir's brother, has made clear since taking power in July it is committed to pushing political and economic reforms in Kuwait, which has one-tenth of global oil reserves.