Papers were filed on behalf of Californian James Clem and on behalf of Hannons Inc., a Maryland company.
Last week, investment firm Berkshire Hathaway Inc. and 3G Capital management said they had reached a deal to buy Heinz for $72.50 per share.
The lawsuits both said that price was "unfair," the Pittsburgh Post-Gazette reported Monday.
"The (Heinz) board ... support the proposed acquisition in order to secure liquidity for their illiquid holdings in the company. From the sale of their illiquid block of shares in the proposed acquisition, the board and company management will receive more than $400 million," court papers say.
The shareholders allege that Heinz's board would not talk with other bidders and included a termination fee of "tens of millions of dollars" in their purchase agreement. That meant Heinz was forced to follow through with the Berkshire Hathaway deal.
A Heinz spokesman declined to comment on the lawsuits, the newspaper said.