Four-times champions Toulouse also failed to qualify for the knockout round when their kicking went to pieces and they were beaten 9-5 by Leicester Tigers in a winner-takes all Pool Two encounter at a wintry Welford Road.
Leinster's slim chances of progressing rested on Munster scoring fewer than four tries in their final Pool One match while hoping pool leaders Saracens would slip up. Saracens hammered winless Edinburgh 40-7 on Sunday to advance.
It is the first time since Wasps in 2008 that the holders have made a pool-stage exit and came the day after Leinster had battled to beat Exeter 29-20 to finish second in Pool Five and keep alive their hopes.
Munster were fired up for their task at Thomond Park and it was made a little easier for them following a sixth-minute red card for Racing flanker Antoine Battut for a knee to the head.
First-half tries for Conor Murray, Simon Zebo and Mike Sherry helped Munster to a 17-6 lead at the interval and Zebo later added two more tries to make sure of the bonus point and keep Munster in the frame for a third Heineken Cup.
"Leinster put on a show last night (against Exeter) and we knew today we would have to put in a big performance and thankfully everyone has put in a serious amount of effort," wing Zebo told Sky Sports.
"We've qualified now so it's great news for the squad."
Munster will travel to Harlequins in April's quarter-finals, while Leicester will play at Toulon. ASM Clermont Auvergne will host Montpellier in an all-French encounter and the other fixture features Saracens at home to Ulster.
Snow and blustery conditions formed the backdrop to the day's key Pool Two clash between Leicester and Toulouse, where the winner was guaranteed to progress.
Leicester had suffered a pre-match blow when England international Manu Tuilagi failed a late fitness test on a leg injury but they nevertheless looked the livelier side.
Leicester's points all came from the boot of Toby Flood in the first half, while Toulouse missed several penalties in bad conditions at Welford Road.
A Yoann Huget try reduced the deficit but Luke McAlister could not convert as Toulouse's bid for a record fifth Heineken Cup came to an end.
"It was a game when it was almost easier to play without the ball," Leicester head coach Richard Cockerill told Sky Sports.
"They missed some kicks at goal, and to be fair to Toby he kicked that one just before halftime to give us a nine-point cushion.
"The effort at the end, those last two minutes with the crowd on their feet, they are magic moments."
Snow was also swirling around at Vicarage Road, where Saracens were playing for the final time before their move to their new Allianz Park stadium.
They made easy work of Edinburgh with five tries - one each for Matt Stevens, Charlie Hodgson and Chris Wyles and two for Chris Ashton - to reach the knockout stage for only the third time.
"It's a great achievement to get through to the quarter-finals again. We had a really tough group and we had to be consistent throughout and we've done that," Saracens director of rugby Mark McCall told the BBC.
The day's other Pool Two match was a dead rubber with Treviso beating fellow eliminated team Ospreys 17-14.