No. If anything, it promoted it, though that also overstates things a bit. The Catholic Church was responsible for basically all learned knowledge in the European Middle Ages, and was one of the reasons that people tried to get educations in the first place. They created the context for organized learning, literacy, and even investigation of the natural world.

The idea of it "holding it back" is total nonsense propagated by 19th century anti-religionists who misread or misunderstood the history entirely.

A really simple example from the late middle ages/very beginning of the early modern period is Copernicus. Copernicus was looking at astronomical problems because the Church asked everyone to do so because their calendar wasn't working so well anymore. Copernicus worked for the Church, came up with a different explanation that made better aesthetic sense to him, and published it (albeit it came out right when he was dying). The Church did not ban his book until hundreds of years later, in the early modern period (when they were worried about a lot of political problems related to the Reformation, Counter-Reformation, etc.).

The European Middle Ages were much more scientifically and technologically diverse and "progressive" than people tend to realize (there was a brief period when everything sort of went to hell, right around the "fall of Rome" period, but after that things started to regularize and normalize until the whole "famines and plague" part of things). It's not coincidental that by the end of the Middle Ages, Europe has the technological and economic and political know-how to take over half of the world! They didn't come up with that stuff overnight.

If you want to look into why things didn't always work out in the Middle Ages, the Church really isn't the culprit. The bigger culprit is the fact that the political, economic, and social situations were pretty dodgy and it's hard to get real things done when things are dodgy. But the Church was, esp. by the late Middle Ages, a major promoter of knowledge. That is not quite the same thing as "science" — what we today think of as science as a profession or even as a method (historians don't think there is one scientific method, but that's another story) had not really been invented or codified yet. But there were learned people, thinking about the natural world — many of them doing so in the context of the Church, or doing so for the reasons of natural theology (i.e., studying the natural world as a form of studying God).

If you want to talk about the Church inhibiting things, you generally have to go to the early modern period (e.g. Galileo) and even then it is more complicated than the Church just being a stick in the mud (most of their "issues" had to do with politics, not science, but sometimes science and politics became intertwined and that could lead to problems for scientists who were in places where the Church had strong influence).

To put it another way, what "progress" would they have held back? The Ancient Greeks had done interesting things with natural philosophy, the Romans did some but were a lot less interested in it, the major Hellenistic centers (like the Library of Alexandria) were destroyed towards the end of their rule. The Byzantines preserved knowledge, the Arabs borrowed and worked on it, and eventually the Europeans got around to getting copies back from the Arabs. This is a short-hand history of things but gives you the rough overview. It's not like things were going in one, unified direction and then the Church came along. Much of what we consider to be the beginnings of "modern science" comes in the so-called "Scientific Revolution," which is in the early modern period, centuries after the end of the Middle Ages.

Entirely separately, it is worth noting that science and technology were not linked in any serious way until a much later period. They were done by different people (e.g. philosophers vs. guildsmen and craftsmen), it is not until relatively recently that they became "joined at the hip" in the way we think of them today. They have very different stories in this time period.