The 12-year-old said most of the awards she received for the Oscar-winning film were destroyed in the blaze on Friday.
She said that she and other members of her family were watching television when they heard shouts of a fire and ran out of their tin-roofed shanty.
"We just grabbed what we could and dashed out. The fire spread so fast we couldn't get back in," said Rafiq Ali, Rubina's father.
Police were investigating the cause of the fire, which left 21 people injured and 2,000 homeless.
Officials said fires are common in Mumbai's slums, and most are sparked by shoddy electrical wiring.
Rubina played the young Latika in "Slumdog Millionaire," the rags-to-riches blockbuster that won eight Oscars.
The Associated Press contributed to this report.