Brumby announced the grant during a Diwali celebration event that attracted thousands of Indians as well as locals in the heart of city's business district.
The event is the largest cultural show managed by company 'Celebrate India' that will also put up a lighting festival competition next week.
Brumby said Diwali was an important occasion for the Indian community and a great example of how Victoria's multicultural communities come together to share their values.
"Diwali is one of India's most significant festivals which cuts across all religious, social and economic differences and is enjoyed by people all over the world," Brumby said.
"It is a festive and vibrant occasion that offers a wonderful combination of revelry and tradition," he said.
Over 100 incidents of attacks on Indians, including racial, have come to light since May last year in Australia and Victoria has seen the highest number of such assaults.
21-year-old student Nitin Garg, who was stabbed to death here, was the first victim of such assaults this year.
The USD 1 million fund would be routed through the Victorian government's USD 12 million Cultural Precincts and Community Infrastructure Fund.
The fund would be given to the Hindu Society of Victoria for the construction of a 'Hindu Cultural and Education Centre' in Carrum Downs.
The proposed facility will be adjacent to Shri Shiva Vishnu Temple, and will include a heritage resource and learning centre, a centre for educational and cultural activities, and catering facilities to be used as a training kitchen.
"This Centre will bolster the strong Hindu community spirit and enhance visitor engagement by broadening and deepening the knowledge about the Hindu faith and community in the area," Brumby said.
"The Hindu Society of Victoria has been steadfast in its commitment to a diverse, yet inclusive Victoria, and this funding will allow for all Victorians to benefit from culturally harmonious society," he said.
The announcement is in addition to a USD 100,000 funding boost for the Hindu community to build a community hall announced by Minister Assisting the Premier on Multicultural Affairs, James Merlino at the Melbourne Vinayagar Hindu Sangam Temple in The Basin.
Brumby said the Victorian Government valued the richness of Indian culture and is proud to contribute funding towards Diwali celebrations across Victoria.