The statement on state news agency SPA said Yemeni tribal mediators had facilitated the release of seven Yemenis held by the kingdom in exchange for a detained Saudi lieutenant, Reuters reports.
An alliance of Arab countries launched airstrikes and a ground offensive against the Houthis on March 26 after Houthis rose to power in what they said was a revolution against corrupt officials beholden to Saudi Arabia and the West.
The conflict had fallen into a stalemate, in which the Houthis still control the capital Sana'a and other major cities in central Yemen.
Saudi state news said the prisoner initiative was launched by Yemeni tribal figures to reduce the violence in the border area and facilitate delivery of badly needed aid, and that the apparent truce could help end the conflict.
"The leadership of the coalition forces welcomed the continuation of a state of calm along the border ... which contributes to arriving at a political solution," SPA said.
On Tuesday, two officials from a Houthi-run government body in Yemen told Reuters that senior representatives of the group had arrived in Saudi Arabia for peace talks.