The state is trying to determine whether the bank and Countrywide Financial had sold the securities to investors under false pretenses, the paper reported, citing a person familiar with the matter.
Bank of America bought Countrywide in 2008, leaving itself with billions in losses from soured loans and lawsuits.
The subpoenas come as state attorneys general and federal officials are negotiating a broad mortgage settlement with Bank of America and other major lenders. California reportedly walked away from those talks two weeks ago, although it is possible the state could still sign onto an agreement.
Bank of America declined to comment to Reuters.
The company's shares were down 2.8 percent at $6.22 in morning trading.
(Reporting by Rick Rothacker in Charlotte, North Carolina, editing by Gerald E. McCormick and Lisa Von Ahn)