North Korea's diplomatic presence in the emirate will also be reduced to a charge d'affaires and three diplomats, the source told AFP, requesting anonymity.
The measures follow a visit less than two weeks ago by Kuwait Emir Sheikh Sabah al-Ahmad Al-Sabah to Washington.
The source said Kuwait will not renew permits given to North Korean workers to re-enter the country after projects they are currently working on are completed "within one or two years".
There are between 2,000 and 2,500 North Korean workers in Kuwait, and thousands more are believed to be working in other Gulf states.
Kuwait has also decided to stop issuing visas to North Koreans and suspend all trade relations and flight links with Pyongyang.
Asian diplomatic sources have told AFP that South Korea and Japan have been putting pressure on Gulf states to stop employing North Korean workers because money they sent home was benefiting the regime.
On Friday, North Korea fired a ballistic missile over Japan and into the Pacific, responding to new UN sanctions with what appeared to be its furthest-ever missile flight amid high tensions over its weapons programme.
UN Secretary General Antonio Guterres condemned the missile test, and said talks on the crisis would be held on the sidelines of the General Assembly meeting next week.
US President Donald Trump and his South Korean counterpart Moon Jae-In have pledged "stronger pressure" on Pyongyang, Seoul said Sunday, after North Korea defied tough new sanctions with the test and said it wanted to match American nuclear strength.
