The attack on Thursday came a day after Saudi authorities accused the fighters, who want autonomy from Sana'a, of killing at least one of their soldiers on the countries' border.
The Reuters news agency reported Saudi officials as saying that the air force had attacked fighters who had seized a border area, killing about 40 Houthis.
The border area was also recaptured.
But a Yemeni defence ministry official denied that Saudi forces had struck targets inside Yemen.
"Saudi Arabia did not hit targets in Yemen," the official said.
Six locations were said to have been hit in Yemen, including one that received about 100 missiles in one hour.
The Houthis, who are primarily from the Zaidi Shia sect of Islam, earlier posted pictures on the internet of their fighters in the Mount Dokhan area inside Saudi Arabia, although they could not be independently verified.
A five-year-old conflict between the Houthis and Sana'a has intensified since August, with both sides increasing attacks.
The conflict has raised potential regional tensions, with the government accusing Iran of supporting the Houthis, while the opposition group has said that Sann'a is too close to Saudi Arabia.
The Houthis want a return to autonomous rule that was ended by a 1962 revolution.
The Houthis say they have been politically, economically and religiously marginalised by the government, which they see as corrupt, while in recent months Sana'a has vowed to crush the rebellion.
Thousands of people have died and tens of thousands have been displaced due to the conflict, according to the Red Cross and the UN.
Source: Al Jazeera (English)