The fighting took place in the Saudi border positions of Shurfa and Jahfan in the southern edge of Jizan, according to al-Masirah TV channel.
The Yemeni forces have killed dozens of Saudi troops and seized control over several posts in Shurfa and Jahfan, the report added.
Fighting has been raging on and off in the southern Saudi border provinces of Jizan, Asir and Najran since 2015.
Saudi Arabia is leading an Arab military coalition that intervened in Yemen in March 2015 and launched an aggression against Yemen in 2015 to restore fugitive President Abd-Rabbu Mansour Hadi.
Yemen’s Army and Popular Forces have expanded their operations in retaliation for the ongoing US-backed Saudi airstrike campaign, which has killed or injured over 60,000 people as of October — as well as the devastating siege which has triggered a borderline famine. Women and children constitute most of all casualties from airstrikes and military operations.