Palin rejected the charge, but launched the so-called "Troopergate" investigation in late July.
The issue could cast a shadow over Palin, who was a shock pick as running mate for John McCain, the Republican candidate for president in the election on November 4.
Stephen Branchflower, the senior investigator, said before the vote that Todd Palin was "such a central figure ... I think one should be issued for him".
Todd Palin, an oil-rig worker and championship snowmachine racer, attends meetings at the governor's office and is copied in on emails concerning state business despite holding no official position.
The committee also subpoenaed Palin's chief-of-staff and deputy chief-of-staff, but had agreed beforehand not to consider such a move against the Republican hopeful on the understanding she would agree to an interview by the investigator.
Under the legislature's rules, the subpoenas must be approved by Lyda Green, the Alaska senate president.
Republican efforts to delay the investigation until after the election were thwarted when Charlie Huggins, a Repubican state senator who represents Palin's hometown of Wasilla, sided with Democrats.
"Let's just get the facts on the table," he said.
The McCain campaign released a statement from Sean Parnell, the Alaska Lieutenant Governor, criticising Democrat politicians.
"I'm disappointed by the complete hijacking of what should be a fair and objective process," the Republican said, calling the investigation a "smear".