FRANKFURT—After 18 months of study, $2,200 in tuition and three exams, Ewa Feix is now permitted by German law to bake two variations of cupcakes.

“Not pretzels, not Black Forest gâteau, not bread,” said Ms. Feix, a Canadian who moved to Germany in 2009. Becoming a professional bread baker entails a three-year apprenticeship and more exams.

Germany’s thicket of rules and standards shields roughly 150 professions from competition, from ski instructors to well-diggers. Stiff fines await uncertified practitioners. German authorities conduct thousands of enforcement raids each year.

Now, the system—rooted in medieval guilds—is under attack.

Many praise Germany’s rigorous apprenticeship model for funneling high-school dropouts into solid middle-income jobs. But economists warn the rigid rules are holding back growth and investment in the services sector, and contributing to the nation’s vast current-account surpluses, long a bone of contention with trading partners.

Crucially, German resistance has also helped stymie efforts to deregulate the vast European Union services market, which accounts for more than 70% of the region’s output but only around one-fifth of internal trade, according to Open Europe, a think tank. Since more productive companies are restricted from moving between countries to take market share, productivity suffers.

In business services, German worker productivity has barely risen since 2001, lagging behind the export-heavy manufacturing sector by about 30 percentage points, according to the Organization for Economic Cooperation and Development. Outside the crafts, Germany also slaps an extra layer of regulation on normally regulated fields including law, accountancy, architecture and telecommunications, the OECD says.

And while protected professions make up only about 10% of Germany’s $3.5 trillion economy, their indirect impact is much broader because services like engineering and telecoms are crucial for other industries, says Andres Fuentes, an economist at the OECD in Paris.

Fully liberalizing the EU services market could deliver a permanent economic boost worth around €300 billion, or 2.3% of gross domestic product, estimates Open Europe.

“The most powerful ‘quick win’ [for the region’s economy] would be to complete the single market, especially in services,” European Central Bank President Mario Draghi said in June.

But strong middle-class support, particularly among Chancellor Angela Merkel’s supporters, means the German system has defied repeated attempts at reform.

Defenders of the German system argue it ensures service quality and helps protect middle-class incomes against globalization, unlike in the U.S. and U.K. The middle classes accounted for about 60% of Germany’s income in 2013, compared with 43% for the U.S., according to a study by Berlin-based think tank DIW.

While anxiety over foreign workers fed the Brexit vote in Britain, German workers worry less about low-wage competition.

“The Brits need the Poles because they can’t do skilled jobs themselves,” said Bernd Ehinger, president of the crafts industry association for the Frankfurt region. His family firm, Elektro Ehinger GmbH, employs more than a dozen Master craftsmen, who each earn more than €60,000 a year.

To set up shop in Germany, plumbers, bricklayers and workers in 39 other crafts must typically pass a three-year apprenticeship course and then take a vocational degree to become a master of their trade. The process takes five or six years.

But the German system also means less competition and higher prices for consumers, said Daniel Dalton, a European lawmaker who compiled a recent report on Europe’s services sector. “Elements of the rules for craftsmen could be described as discriminatory,” Mr. Dalton said. “I worry that some are protectionist.”

While many European countries regulate professional services, the practice is most pronounced in Germany, where a third of workers require a professional certificate to perform their job, compared with 14% of Danes and 19% of Brits, according to a survey by the European Commission, the EU’s executive arm.

The Commission this year stepped up legal proceedings against Germany for limiting competition in certain professional services, including architects and engineers. It plans to make fresh legislative proposals later this year aimed at making it easier for EU professionals to set up shop in other countries and offer their services across national borders.

Meanwhile, the arrival of more than a million migrants is putting fresh pressure on Berlin to ease their route into well-paid jobs. A failure to properly integrate the newcomers, who are typically keen to set up businesses, could seal Chancellor Merkel’s political fate.

Germany places 107th in the World Bank’s ranking of countries where it’s easiest to start a business, below Guatemala and Sierra Leone.

Germany’s traditional approach to job qualifications “may not work well for refugees (or other immigrants), who are often older than typical trainees, may have skills learned informally, and may not be able to afford lengthy schooling periods with low earnings,” the International Monetary Fund said in June.