BERLIN—Europe’s biggest economy needs people who think small.

German business is booming and employment stands at a record high. But the surge is driven mainly by decades-old companies. Startups are scarce and getting rarer. That worries policy makers.

In a sign of how seriously the government takes the country’s dearth of entrepreneurialism, left-leaning Social Democrat Economics Minister Sigmar Gabriel is pushing to expand tax breaks for startups and trying to ease their path to the stock market.

Mr. Gabriel announced plans last month that could boost the appeal to private-equity funds of investing in German startups. He proposed allowing companies to cut their tax bills by claiming losses over many years and carrying them even after a buyout.

A few weeks earlier, Mr. Gabriel told a meeting of entrepreneurs, investors, banks and stock-market officials he aimed to promote public listings of growing firms. “It is important to me to make the bourse again an important source of financing for young, fast-growing companies,” he said after the meeting.