The Australia cricket great, currently in England where he is commentating for broadcaster Channel 4, made his comments after witnessing Bangladesh's innings and 261 run defeat in the first Test at Lord's.
The match, Bangladesh's first Test in England, finished before lunch on the third day here Saturday with Benaud labelling it an "absolute shambles".
Benaud, writing in the News of the World, Britain's biggest selling Sunday tabloid, was adamant that the presence of Bangladesh - whose only win in 37 Tests has come against fellow strugglers Zimbabwe - was neither good for the game as a whole or for the teams themselves.
"After witnessing this two-and-a-bit day farce at Lord's, I am convinced our game's governing body - the International Cricket Council - must make a firm and swift decision," Benaud said.
"They must remove Bangladesh and Zimbabwe from full-time international cricket until their ability and infrastructure warrant their re-inclusion.
"Both teams need to be put on hold for the good of cricket. They are simply not good enough to be pitched against proper Test match countries."
Benaud added: "What should be done is to have both countries scheduled to play a carefully programmed series of matches against A teams and minor teams from the other eight (Test) countries and they should play against one another as well."
"They can undertake short tours where none of the opposition will be of international standard and we can see if they are improving, standing still or going backwards."
The ICC is due to hold its annual meetings at Lord's in June.
However, it is unlikely that the standing of either Bangladesh or Zimbabwe will be on the agenda given that the governing body has repeatedly said the duo's Test status is not up for discussion.
Benaud, 74, one of cricket's best-known broacasters, was the first player to complete the all-round double of 2,000 Test runs and 200 Test wickets.
The leg-spinner led Australia in 28 of his 63 Tests and never lost a series as captain.