No.
Of course there exist locations in the world where microplastic will be found in the water -- given the standards in some parts of the world, this cannot be doubted -- but overall the claims are most certainly (in the case of Germany provably) wrong, and intentionally misleading.
The article you linked to is not a study but a sensational article which fails to provide any hard facts or sources (although there is a "study" from the same source as well, hard to find as it is).
The articles in Der Spiegel and WDR mentioned in another answer actually doubt the validity of the forementioned study, citing an expert from the Federal Environmental Agency who provides a couple of excellent arguments why the study results are (at least for Europe and in particular Germany) doubtful. The most compelling argument is that 80% of our drinking water comes from deep ground water, which, by passing through sediment, has been filtrated to the point of being naturally sterile.
As a funny anecdote, Der Spiegel cites The Guardian and BILD as sources, both of which are not precisely well-known for high-quality journalism or factual accuracy. There exists the well-known proverb: "BILD talked with the dead" to account for their habit of publishing unbelieveable and completely false stories (followed by tiny dementi on page 6 or 7 in the next issue) regularly.
The actual study done by ORB Media disqualifies itself in the abstract by making a claim that is outright impossible for Germany:
Most these particles [sic] were fibers (99.7%), between 0.1 - 5 mm in length.
The law ("Trinkwasserverordnung" in Germany, but other EU countries have similar laws) requires a threshold of zero on several germs (E. coli among them), with technical filtration if need be. Which effectively means unless you already have exclusively deep ground water filtered appropriately by nature, water suppliers must run their water though a filter none larger than 1.2µ to comply with the law. There are many more requirements (all of which I will not go into detail), among them a maximum cloudiness, which also factually implies filtration on a single-digit micrometer scale.
Some sources for actual ("in use") filter sizes for preparing surface water as drinking water in the 0.1 to 3µm range and 5µ/1µm prefilters followed by nanofiltration: [1], [2]
The supplier regularly needs to provide evidence of compliance, and penalties are harsh, to say the least.
Additionally, the overwhelming majority of households (and public buildings) have additional filters installed in the basement meant to hold back the odd scrap that might come from the water pipe. Those are not meant to hold back bacteria, but have a pore size anywhere from 5µ to 20µ.
Thus, the claim of having found particles 0.1-5mm in size (which is 100 to 5,000µ) in roughly 3/4 of the samples is, disregarding the possibility of having contaminated the samples, beyond "unlikely" but outright ridiculous.
The "Methods" section states, among other things, that samples were in some cases collected by scientific partners and in some cases by non-scientific partners (read as: laymen), as well as Orb staff and volunteers (again: laymen) using plastic bottles which were then sent across the globe by mail. That methodology provides for an excellent opportunity to contaminate the samples.
Evidence for microplastic was obtained by colorizing the residue on a 2.5µ filter with a pigment which binds to organic material. Thus followed prodding residue with a stainless steel spatula, if it didn't break, plastic was assumed. Again, the methodology is somewhat doubtful as hard evidence.
