According to the source, Russian citizens are gathering in Sanaa's airport waiting for the plane's arrival.
Earlier in the day, a source in Cairo's airport told RIA Novosti that the Russian aircraft was given a go-ahead to fly.
Last week, an international coalition headed by Saudi Arabia launched a military operation against Houthi positions in Yemen following a request for military support from Yemeni President Abd Rabbuh Mansur Hadi.
The Houthis have recently taken control of the Yemeni capital Sanaa, forcing the president to flee the country, and making rapid advances into other cities.
Foreign countries and international organizations, including the United Nations, have been evacuating their citizens and staff from Yemen amid the intensified conflict.
