The deal prices Rubio's outstanding stock at $8.70 per share, which is a 14 percent premium to the company's Friday closing stock price of $7.66. Mill Road currently owns about 5 percent of the restaurant operator's shares.
The board unanimously approved the acquisition, which is expected to close in the third quarter.
Rubio's said in October that it was looking into its strategic options, including a potential sale of the company.
Shares of Rubio's Restaurants rose 84 cents, or 11 percent, to $8.50 and reached a 52-week high of $8.60 in earlier trading Monday.