He did not explicitly refer to the kingdom's regional rival Iran but Saudi officials have accused Tehran and the Lebanese militant group Hizballah of aiding rebels in Yemen.
"We will not accept any interference in the internal affairs of Yemen," King Salman said in an address opening a new session of the Shura Council, an appointed body which advises cabinet.
Salman said his country will neither accept that Yemen "becomes a base or a point of passage for whatever state or party to menace the security or the stability of the kingdom and of the region".
The Saudi-led coalition intervened after Houthi rebels allied with elite members of security forces loyal to Yemen's former president Ali Abdullah Saleh seized the capital Sanaa and overran other parts of the country.
The rebels have killed at least 110 civilians and soldiers in rocket fire and skirmishes along the Saudi frontier. They have also fired longer-range ballistic missiles over the border at Saudi Arabia.
International investigators last month said they had found a suspected "weapons pipeline" from Iran through Somalia to Yemen.
British-based Conflict Armament Research, which is primarily funded by the European Union, analysed photographs of weapons including assault rifles and rocket launchers to draw its conclusions.
Tehran has repeatedly denied sending arms to Yemeni rebels.
The Arab coalition, for its part, has faced repeated allegations of killing civilians, and on Tuesday the United States blocked the transfer of precision-guided bombs to Saudi Arabia.
Since March 2015, Saudi Arabia has itself led an Arab coalition conducting airstrikes against the Houthi rebels and providing other assistance to local forces in support of President Abedrabbo Mansour Hadi.
