Speaking to a small group of reporters at the Iowa Renewable Fuels Summit in Altoona, where several 2016 presidential candidates are slated to speak, Branstad labeled Cruz a "big oil" candidate whose victory would be "very damaging to our state."
"It would be a big mistake for Iowa to support him," Branstad said. "And I know he's ahead in the polls but the only poll that counts is the one they take on caucus night and I think that could change between now and then."
Asked by a reporter whether he wants to see Cruz defeated, Branstad answered: "Yes."
Branstad's attack on Cruz is an extraordinary intervention in the caucus campaign. The state's caucuses take place on February 1.
"I don't think it's a foregone conclusion that Ted Cruz is going to win this state," Branstad told CNN afterwards. "Because as Iowans learn about his anti-renewable fuel stand, and that it will cost us jobs, and will further reduce farm income, I think people will realize that it's not in our interest."
He added: "I don't think that Ted Cruz is the right one for Iowans to support in the caucus."
Cruz's stance on ethanol subsidies has emerged a significant vulnerability for the senator in Iowa, a state where farming and agriculture are hugely influential industries. His rivals -- particularly Donald Trump -- have been hitting Cruz hard for his opposition to ethanol subsidies, and voters here have expressed concerns about Cruz's rejection of ethanol subsidies.
Branstad's son, Eric, works with the group America's Renewable Future, which has targeted the Texas senator.
Speaking with CNN's Jake Tapper on "The Lead" last week, Branstad said Cruz has the best "ground game" in the Hawkeye State, but added that the Texas senator's stance on renewable fuels could "really hurt him here."
"He's opposed to the wind energy tax credit. He's opposed to ethanol and biodiesel. And we have tens of thousands of jobs and a lot of farm income dependent on that," Branstad said. "And I know there's a lot of people working in those ethanol refineries and farmers that are not going to vote for somebody that opposes something that's so important to our state's economy."
Cruz has been leading in some recent Iowa polls, and Trump is his closest competition, and the real-estate mogul quickly pounced on Branstad's statement Tuesday afternoon.
"Wow, the highly respected Governor of Iowa just stated that 'Ted Cruz must be defeated.' Big (shocker)! People do not like Ted," Trump tweeted.
Iowa governors have typically stayed neutral in the caucuses, and Branstad did not endorse a candidate in the 2012 Iowa contest. In 2008, Gov. Chet Culver, a Democrat, did not pick sides between Hillary Clinton and Barack Obama.