"Houthi rebels opened fire on the minister's motorcade as he left the house of President [Abd Rabbuh Mansour] Hadi," the source, requesting anonymity, told The Anadolu Agency.
He said that the minister was unhurt in the attack.
The failed attempt came as clashes broke out near Hadi's house between presidential guards and Houthi militants in Sanaa.
Yemen has been suffering lawlessness since a popular uprising that erupted in 2011 ended the autocracy of President Ali Abdullah Saleh a year later.
The Houthis seized control of Sanaa in September of 2014 and have since then moved to extend their control to other provinces.