Libby, who could face up to 30 years in prison, resigned minutes after the indictment was handed up in federal court in Washington.
In a statement, Cheney said Libby would "fight the charges brought against him."
US President George Bush's top political adviser, Karl Rove, was not indicted along with Libby, but special counsel Patrick Fitzgerald has made clear to Rove he remains under investigation and in legal jeopardy, lawyers said.
Libby's indictment and resignation was another setback to a White House already on the defensive over the bungled initial response to Hurricane Katrina, growing opposition to the Iraq war and the withdrawal of Bush's nominee for the US Supreme Court, Harriet Miers.
At a news conference after the grand jury acted, Fitzgerald said his investigation was continuing but he declined to discuss anyone who was not charged.
"It's not over," he told reporters.
Despite initial denials, both Rove and Libby spoke to reporters in June and July 2003 about the CIA operative, Valerie Plame, whose identity was leaked to the media.
Libby, who played a major behind-the-scenes role in building the case for the Iraq war, was accused in the five-count indictment of making false statements about how and when he learned and disclosed to reporters classified information about Plame.
Libby was not charged with illegally disclosing the name of a CIA operative. The charges were the first brought as part of the investigation.
If convicted, Libby, 55, faces a maximum sentence of 30 years in prison and a $1.25 million fine, prosecutors said.
The charges accuse Libby of lying to FBI agents who interviewed him on October 14, 2003, and November 26, 2003, committing perjury while testifying under oath to the grand jury twice in March 2004, and engaging in obstruction of justice by impeding the grand jury's investigation.