Houthi media, citing an anonymous military official, renewed threats on Sunday against Saudi oil giant Aramco and aviation in the kingdom.
Yemen's Houthis, fighting a Saudi-led coalition backing the internationally recognised government, are allies of Iran, which on Sunday warned the US and Israel not to renew strikes on the Islamic republic after they had threatened a return to war.
"Aramco facilities are within range of the Yemeni Armed Forces, and investments in them are a venture fraught with losses," the Houthis' Saba news agency quoted the military official as saying.
The official also warned international airlines against using Saudi airspace "except for the airspaces of Mecca and Medina".
The Houthis have targeted oil facilities and airports in the kingdom since Yemen's once-dormant war reignited in July, killing 24 people in Saudi Arabia last month.
An October 10 strike on Riyadh's international airport became the deadliest on Saudi soil in years when it killed at least 13 people.
Meanwhile, fighting in Yemen has displaced more than 300,000 people in the western part of the impoverished country.
Most of them forced from their homes in the last two months, the displaced "urgently need shelter, food, clean water and health care", the International Organization for Migration said in a statement on Sunday.
The United Nations says more than 1,600 people have been killed since fighting in Yemen reignited.
Saba on Sunday said that Saudi Arabia had "targeted the Faculty of Medicine at Hodeidah University with two raids", and two Hodeidah residents told AFP they heard an explosion in the area.
A fragile 2022 truce fell apart in July after the Houthis allowed an Iranian plane to land in Yemen's capital Sanaa in defiance of Saudi control over Yemeni airspace, setting off a spate of attacks.
