Saudi daily al-Sharq al-Awsat and a number of other outlets claimed on Sunday that the Houthis have prevented a charity society in the city of Amran, west of the country, from holding Quran teachings sessions in the city.
They alleged that the Ansarullah movement has told the society they can teach everything except memorization of the Quran.
The movement has denied the accusations.
Earlier this week, Saudi Arabia claimed it had intercepted a ballistic missile launched from Houthi-controlled territory in Yemen toward Mecca.
They claimed Houthi fighters launched a Scud missile from Saada province toward Mecca at 21:00 local time (18:00 GMT) on Thursday.
The Houthis confirmed the launch of a Scud-type ballistic missile known as Burkan-1 into Saudi Arabia, but said the projectile was targeting the city of Jeddah – not Islam’s holiest city, which lies just over 60 kilometers (37 miles) away.
Since March 2015, Saudi Arabia and some of its Arab allies have been launching deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to the fugitive former President Abd Rabbuh Mansour Hadi, a close ally of Riyadh.
They have failed to achieve their objective, but nearly 10,000 Yemenis, including 4,000 women and children, have lost their lives in the deadly military campaign.