Warplanes carried out more than 30 strikes overnight on the northwestern Yemeni provinces of Saada and Hajja near the border with Saudi Arabia, local officials and residents said on Wednesday.
The strikes occurred after Yemen's Houthi fighters fired mortar bombs and rockets at a Saudi Arabian border town on Tuesday for the first time since a Saudi-led coalition began a military campaign against them on March 26.
Saada is a stronghold of the Iranian-allied Houthi movement.
Houthi sources said 43 civilians were killed and at least 100 wounded as a result of the strikes, which lasted until dawn on Wednesday. The figure could not be independently verified.
Local sources also said there was heavy artillery shelling coming from the Saudi border.
In Tuesday's bombardment, projectiles had struck a girls' school and a hospital in Saudi Arabia's Najran town, only 3 km (2 miles) from Yemen's border.