Kenny Jackett's side arrived at the King Power Stadium without a league win in 10 matches but Henderson's treble - the first from the penalty spot - halted Leicester's four-game winning run at home.
After seeing his team move to within a point of the play-off places with victory over Watford in midweek, Sven-Goran Eriksson named an unchanged starting line up.
Jackett made two changes from last weekend's draw against Brighton as Alan Dunne and Jack Smith came in for Scott Barron and Tamika Mkandawire.
Leicester almost took a first-minute lead. Sol Bamba got on the end of a Richie Wellens corner but the big defender's header was parried by Millwall goalkeeper David Forde.
The visitors looked short of confidence. David Nugent had a couple of chances but shot wide and then over the crossbar with a overhead kick. Yuki Abe sent an effort from the edge of the area whistling past the post.
Millwall briefly threatened when Henderson forced Kasper Schmeichel to get down and save his shot from outside the box.
It was against the run of play when Jackett's men went ahead after 36 minutes. Bamba was adjudged to have fouled Brian Howard and Henderson blasted home the resulting penalty. Schmeichel got a hand to the ball but could not keep it out.
Wellens worked Forde again from 18 yards before Millwall caught out Leicester again in first-half stoppage time.
Nadjim Abdou crossed from the right-hand side and Henderson was on hand to tap home from close range.
Eriksson replaced Abe and Jermaine Beckford with Lloyd Dyer and Darius Vassell at half-time and Leicester looked sharper.
They were almost back in the game straight away but Lee Peltier's 12-yard effort struck the crossbar.
Dyer narrowly missed with a shot from just inside the area before Michael Johnson fired over.
Just as in the first half, Leicester were the better side but could not take their chances. And just as in the first half, Henderson made them pay.
The striker completed his hat-trick in the 68th minute. Leicester left him unmarked at the far post and Henderson headed home Liam Feeney's corner.
Schmeichel had to get down to smother another effort from Henderson 10 minutes later.
Nugent desperately smacked a long-range free-kick over the crossbar before forcing Forde into a routine save with three minutes remaining.