In response, Doug Heye, spokesman for House Majority Leader Eric Cantor, said: "No proposed ENLIST amendments to NDAA will be made in order."
Heye said no stand-alone vote on the measure would be permitted, either.
It was the latest setback for President Barack Obama's efforts to move comprehensive immigration legislation through Congress to boost border security, remake legal worker programs and offer legal status to the estimated 11.5 million people now living here illegally. The Senate passed an immigration bill last year, but it's been stalled in the GOP-led House.
Denham's measure was widely popular and seen as perhaps the likeliest area for compromise.
But in recent weeks prominent conservative groups, including the Heritage Foundation, announced their opposition. Heritage Action, the group's political arm, announced it would include the vote in its ratings on lawmakers and called Denham's legislation "deplorable."
Cantor himself, who previously had supported offering a path to citizenship for immigrants brought illegally as children, faces a primary challenge in Virginia June 10 from a tea party opponent who has criticized the majority leader for not being conservative enough and accused him of supporting amnesty for immigrants living here illegally.
Dave Brat, an economics professor at Randolph-Macon College, is a long-shot to unseat Cantor, but his campaign has won attention and support from conservative leaders such as radio host Laura Ingraham, partly because of his attacks against Cantor over immigration.
Cantor, House Speaker John Boehner and other House GOP leaders have insisted they want to advance immigration legislation, though they've rejected the Senate's comprehensive bill. Chances have always looked slim, but the White House and outside advocates saw a window for action over the next several months, before Congress' August recess and November midterm elections.
Friday's developments seemed to all but rule out anything happening on the issue this year in the House, if even Denham's limited measure could not advance. Despite a wide coalition of business, labor, religious groups, farmers and others pushing for an immigration overhaul, many individual Republican House members who represent largely white districts have been unmoved.
Asked Friday if Boehner disagreed with Cantor's decision, Boehner's spokesman, Michael Steel, said he did not.
Denham's office had no immediate reaction to Cantor's announcement. But in an interview beforehand, Denham, who has a competitive race in his heavily Latino district in central California, said he would keep pushing his legislation regardless of what leadership did.
"I am prepared for a long-term fight on this," he said.
Denham's bill would allow immigrants who were brought to this country on or before Dec. 31, 2011, and were younger than 15 years old to become legal, permanent residents the first step toward citizenship through honorable service in the military.
It was co-sponsored by 50 House members, 26 Democrats and 24 Republicans, but an outspoken minority was opposed. Rep. Mo Brooks, R-Ala., had warned that "all hell will break loose" if Denham tried to promote the measure.
The Senate could still revive the issue if the Senate Armed Services Committee includes the ENLIST Act in its own version of the defense policy bill, something Sen. Carl Levin, D-Mich., the panel chairman, has indicated was possible.