"[He] left capital Sanaa for Saudi Arabia, where his family lives," the source told The Anadolu Agency.
The source said that bin Mubarak's departure had been shrouded in secrecy.
Local media earlier said that Houthis had stipulated that bin Mubarak leaves the country after his release.
Bin Mubarak was released earlier this week by the Shiite Houthi group after being kidnapped earlier this month.
Yemen has remained in the throes of political turmoil since autocratic President Ali Abdullah Saleh stepped down in 2012 following a months-long popular uprising against his 33-year rule.