Hague along with Russian cosmonaut Aleksey Ovchinin had a close brush with death when their Soyuz rocket failed minutes after blast-off from Baikonur cosmodrome in Kazakhstan in October last year. They were forced to eject and make a harrowing emergency landing.
It was the first such accident in Russia's post-Soviet history.
In a decree released on Tuesday, the Kremlin commended 44-year-old Hague for his "courage and high professionalism" shown during life-threatening conditions.
After the accident Hague and Ovchinin successfully launched to the International Space Station aboard another Soyuz rocket in March and returned to Earth last week.
The Order of Courage is one of Russia's top state awards and is often given posthumously.
Space exploration is one of the few areas in which cooperation between Russia and the United States has not been undermined by tensions over Ukraine, Syria and elsewhere.