Skipper Andy Balbirnie contributed 21 before he fell to seamer Jan Frylinck attempting to force the pace.
Only 54 runs came off the last 10 overs with Ireland's next seven batsmen all failing to reach double figures.
Frylinck finished with 3-21 with David Wiese, who played for South Africa at the 2016 World Cup, claiming a respectable 2-22.
As well as securing the last place in the Super 12 stage, the winners will be guaranteed a spot in the 2022 tournament in Australia.
Both teams went into Friday's match with two points after wins over the Netherlands but they came up short against 2014 champions Sri Lanka who top Group A and have already made the next round.
Ireland have not reached the second round since 2012 while Namibia, ranked a lowly 19 in the world, are playing in the tournament for the first time.