According to the Justice Department complaint filed in federal court in San Jose, Calif., the agreement was in place from 2006 to 2009. Intuit is already subject to a settlement barring it from making such agreements.
The California lawsuit would allow the state to recover damages and ensure that the companies do not engage in such conduct in the future.
California's lawsuit lists Intuit as a co-conspirator.
"If California is going to continue to be the high-tech capital of the world, we can't allow anticompetitive conduct that prevents talent from going where it's put to its highest use," Harris said in a statement.
Intuit spokeswoman Diane Carlini said the company is not named in the federal lawsuit and has resolved issues stemming from a similar complaint filed against it and other Silicon Valley companies in 2010.
"This is an eBay matter," Carlini said of the federal lawsuit filed Friday.
eBay, the online auction site, was not part of the previous case.
Carlini said Intuit, which operates a variety of online financial services that include TurboTax and the personal finance software Quicken, is cooperating with the attorney general's office in the separate state lawsuit. But she said any complaints about the company's past recruiting practices have been resolved.
"We don't believe we have any issues," she said.
eBay's revenues in 2011 were $11.7 billion. Intuit's 2011 revenues were $3.85 billion.
Associated Press writer Tom Verdin in Sacramento, Calif., contributed to this report.