Saudi Arabia and its allies struck a day after Saleh's son vowed to lead a campaign against the Houthis.
The intervention by Ahmed Ali, a former leader of the elite Republican Guard once seen as a likely successor to his father, gives the anti-Houthi movement a potential figurehead after a week of fighting that saw the Houthis rout Saleh's supporters in the capital.
Yemen's war, pitting the Houthis who control Sanaa against a Saudi-led military alliance backing a government based in the south, has brought what the United Nations calls the world's worst humanitarian crisis.
Saleh had helped the Houthis win control of much of the country's north, including Sanaa, and his decision to switch allegiances and abandon the Houthis in the past week was the most dramatic change on the battlefield in years.
But the Houthis swiftly crushed the pro-Saleh uprising in the capital.
Coalition fighter jets carried out dozens of air strikes, both sides said, bombing Houthi positions inside Sanaa and in other northern provinces.
Yemen's pro-Houthi Al Masirah television station said the coalition bombed Saleh's residence and other houses of his family members.
Residents told Reuters loud explosions were heard in downtown Sanaa.
Masirah said air strikes also hit northern provinces including Taiz, Haja, Midi and Saada. There was no immediate word on casualties.
In a sign of support and defiance, tens of thousands of Houthi supporters staged a rally in Sanaa on Tuesday to celebrate the death of Saleh. They chanted slogans against Saudi Arabia and its allies.
The death of Saleh, who once compared ruling Yemen to dancing on the heads of snakes, deepens the complexity of the multi-sided war.
Much is likely to depend on the future allegiances of his loyalists, who had previously helped the armed Houthi group.