Video footage from the funeral of a Houthi political leader shows agitated crowds, as a loud blast is heard, followed by the sight of black smoke billowing in the vicinity.
On Saturday, Houthis staged a large-scale funeral for the two commanders in Sanaa, in a display of military strength.
Yemen's Houthi movement fired ballistic missiles at what it called "economic and vital targets" in the southern Saudi province of Jizan on Saturday, and Saudi authorities said a man was killed by debris from the projectiles.
The attack appeared to be retaliation promised by Yemen's dominant political faction, as thousands attended a funeral in the Houthi-run capital Sanaa for a top Houthi official killed in a Saudi-led air strike last week.
Jizan civil defense spokesman Colonel Yahya Abdullah Al-Qahtani said on Arabiya TV that the Saudi national was killed by "falling fragments of military projectiles".
The Huthi rebels' Al Masirah television reported Saturday they had fired eight missiles at "economic and vital targets", a day after Saudi defence forces said they had downed a missile headed for the same area.
The missiles were headed towards the city of Jizan, according to a coalition statement.
Both sides have fought to a stalemate after more than three years of war in Yemen.
The campaign by the coalition against the Houthis has seen more than 16,000 air raids launched across the country since March 26, 2015.
The rebels have seized control over much of the country's north since September 2014, including the capital Sanaa, and forced President Hadi and his government into exile in Riyadh, the capital city of Saudi Arabia.
The kingdom's Arabiya TV quoted the Saudi defence ministry as saying four missiles bound for the province had been intercepted.
Riyadh and its close ally Washington accuse Iran of arming the Huthis, which Iran denies.
Yemen now stands on the brink of starvation.
The militia group has stepped up its missile attacks into Saudi Arabia following the death of two of its leaders as a result of a Saudi-led coalition airstrike.
Tehran has blamed Saudi Arabia for the war, which has unleashed what has been described by the United Nations as the world's worst humanitarian crisis, with the country now on the brink of starvation.