Thursday's doodle depicts the Mangalyaan probe, which has been studying the planet's atmosphere.
Only the US, Russia and Europe have previously sent missions to Mars.
India has succeeded on its first attempt - an achievement that eluded even the Americans and the Soviets.
Mangalyaan - more formally referred to as Mars Orbiter Mission (MOM) - was launched from the Sriharikota spaceport on the coast of the Bay of Bengal on 5 November 2013.
Last month the satellite joined four other missions that are circling the planet: Maven (US), Mars Odyssey (US), Mars Reconnaissance Orbiter (US) and Mars Express (Europe).
At 4.5bn rupees ($74m; Â£45m), Mangalyaan is also one of the cheapest interplanetary space missions ever.
Google doodles, which began in 1998, depict famous and lesser known notable people, events, anniversaries and tributes.
Google has done a number of doodles on a variety of Indian subjects, including marking the country's Independence and Republic Days, the festivals of Holi and Diwali, the cricket World Cup and the birth anniversaries of Mahatma Gandhi and Rabindranath Tagore.
Google has marked the success of India's Mars mission in its famous daily doodle, exactly one month after a robotic probe went into orbit around the red planet.