In the lawsuit filed Wednesday, the academy claims it has the right to buy the historic statuettes and one owned by her late husband for $10 each.
The academy contends an heir to the Oscars demanded $500,000 for one statuette alone in July - an offer the academy refused.
Pickford won the Academy Award for best actress in 1930 and was given an honorary Oscar in 1975.
When she died in 1979, they went to her one-time husband, Charles "Buddy" Rogers, the lawsuit said.
In 1986, Rogers won the academy's Jean Hersholt Humanitarian Award, and when he died all three awards went to his second wife, Beverly.
She died in January, leaving the statuettes to her heirs, who are co-executors of her estate.
The lawsuit names three of the heirs, in their roles as co-executors. It alleges anticipatory breach of contract.
The suit claims that academy bylaws dating from 1950 and agreements signed by Oscar winners give the academy the first chance to buy Oscars for $10 if they ever go on the market.
"If the public believes that any multimillionaire can buy an Oscar, then it becomes cheapened," David W. Quinto, an attorney representing the academy, said Friday. "It becomes an article of commerce rather than a very prestigious award."
Quinto said Pickford was a founder of the academy and helped approve the Oscar design.
"From the academy's point of view it's just unthinkable that Mary Pickford ... would ever consent to do anything that would ever cheapen it in the eyes of the public," he said.
A call to John Shevlin, an attorney representing Beverly Rogers' estate, was not immediately returned.