I don't know about how you could stop it emerging, but if it failed to appear it would make Christianity less resilient to attack. I read somewhere that one of the reasons that North Africa so quickly collapsed in the face of the Muslim invasions and lost its religion so fast after that is that they didn't have a monastic tradition there to help safeguard it. So you could see the same thing happening elsewhere, for instance perhaps the Muslims are able to at least maintain a significant foothold in Iberia as a larger portion of the populace converts from Christianity.
It could also increase centralisation in the Church, as the monastic communities and their leaders always had a great deal of autonomy so by removing them much of the Church's theology might not even come about and you might see a far more united Church. Of course, the Church may well be smaller as the monks played a very important part in spreading Christianity throughout pagan Europe.
In terms of knowledge, the monasteries were important as centres of learning and helped a great deal in preserving knowledge. Without them, the comparatively smaller libraries of the nobility and regular clergy will be all that is left. Many more ancient works would probably be lost to us. There would be far, far few books produced before the invention of the printing press and so knowledge would be even more limited to the upper echelons of society. On the flip side, the need for large numbers of scribes may be filled by a kind of new class who help strengthen the middle class of the period and more evenly distribute power, perhaps even eventually becoming the nucleus of the modern state at an earlier point than OTL as the rulers concentrate the scribes in their hands (although I think such an outcome unlikely at best). In the field of exploration, some monks like St Brendan the Navigator went off and discovered new places. Without them it may take longer to fill in the map of the known world.
After the Dissolution of the Monasteries in England, levels of charity given to the poor didn't recover until the Elizabethan period (if I remember correctly) so many of the peasants of Europe could well be worse off. I would expect the nobility and the rest of the Church to take up some of the slack, but neither group was quite so dedicated to it compared to the monks in my opinion.
All in all, I think it would be worse for Europe as a whole (not even counting all the beautiful monasteries that would never be built).