Read MoreThe young & the restless: Activism's rising stars
Robbins, a former partner at major private equity firms KKR and General Atlantic, said that the Short Hills, New Jersey-based Investors Bancorp is misunderstood because of its relatively complicated structure as a "mutual holding company" and large cash reserves.
Robbins said the New York-area bank has grown significantly over the last 10 years under a strong management team and has accumulated about $2 billion in cash. He called its balance sheet a "fortress."
He recommended the bank use that excess capital to do stock buybacks and increase dividends, benefiting shareholders and, later, acquire other businesses to grow. Once the money is spent, Robbins said, the bank will still have a valuation similar to its peers.
Robbins also said the bank could be an attractive acquisition target itself, another way the stock price could shoot up. He said the stock, which currently trades at nearly $12 a share, could be worth $19.25 by 2019. Blue Harbour owns 7.8 percent of the stock, which is a new position and was publicly disclosed for the first time Monday.
Read MoreDruckenmiller: This could end 'very badly'