"What's going to happen to people like us?" asks the young woman in a sometimes-shaky voice, after identifying herself as immigrant who was brought to the country undocumented as a child.
"Violating the laws has consequences," said Cruz, among the front-runners for the Republican nomination for the November presidential election.
"And one of the problems with our broken immigration system is that it is creating human tragedies," he added.
A video of the exchange was shared by the Democratic Party, which identified the event as a Wednesday campaign stop in Storm Lake, Iowa.
Immigration has become a hot-button issue not only in the campaign generally but particularly for the Republicans and for Ted Cruz, a Cuban-American senator from Texas.
New York businessman Donald Trump, who is leading the Republican pack, launched his White House bid by promising to build a wall along the Mexican border to clamp down on immigration.
He has also suggested a ban on immigration by Muslims in the wake of recent attacks around the world.
Trump has support from 42 percent of his party, compared with 14 percent for Cruz, according to a five-day rolling poll from Reuters/Ipsos dated Jan. 5.
But Cruz now leads his party in the key state of Iowa, which holds the first voting contest for the nomination in the country.
In the past few days Trump has attacked Cruz's Canadian birth, saying it could be a "big problem."
Presidents must be "natural-born citizens" under the U.S. Constitution. Cruz was born in Calgary, Alberta, but his mother was a U.S. citizen, which he says meets the requirements to run.