His comments continued what has become a running dispute between Woodward, perhaps the country's best-known print journalist, and the Democratic White House over who is responsible for the across-the-board cuts scheduled to begin on Friday.
Last week, Woodward published an opinion piece in the Washington Post - where he is an associate editor - saying the administration was "wrong" to blame the cuts on Republicans.
That drew retorts from White House press secretary Jay Carney, who in posts on Twitter and later in comments to reporters blamed the budget stalemate on Republican opposition to including increased revenues in any deal to replace the cuts.
The $85 billion across-the-board budget cuts were mandated by Congress and the White House as part of the August 2011 deal to avoid a government default. The reductions are split between defense spending and domestic programs.
Woodward, who first gained fame in the 1970s from exposing the Watergate scandal during the administration of President Richard Nixon, wrote a detailed account in his 2012 book, "The Price of Politics," of the August 2011 deal that led to the cuts.
On Wednesday he attacked Obama for drawing national security into the budget debate.
"So we now have the president going out (saying) 'Because of this piece of paper and this agreement, I can't do what I need to do to protect the country.' That's a kind of madness that I haven't seen in a long time," Woodward told MSNBC on Wednesday.
On Tuesday, Obama warned of threats to Navy readiness in a visit to the Newport News Shipbuilding shipyard in Virginia, where maintenance to the aircraft carrier USS Abraham Lincoln has been delayed by the budget crisis.
Earlier this month, the Pentagon said it was delaying deployment of another carrier, the USS Harry Truman, to the Middle East because of funding.
Obama's decision to drag the military into the budget fight likely would not have happened in previous administrations, Republican or Democratic, Woodward added on MSNBC's "Morning Joe" program.
(Reporting by Susan Heavey; Editing by Fred Barbash and Eric Beech)