The experts, who advise the government on economic policy, said they expected Germany's economy to grow by 1.6 percent this year and 1.5 in 2019.
That was well below their previous forecast of 2.3 percent and 1.8 percent respectively.
"The uncertain future of the global economic order and unavoidable demographic change represent major challenges to the German economy," said chairman Christoph Schmidt in the council's latest annual report.
The so-called "wise men", actually four men and one woman, urged Chancellor Angela Merkel's government to take action to prepare Germany for the threats ahead.
The warning comes as Germany braces for a period of political turbulence at home following Merkel's announcement that she will step down as head of her centre-right CDU in December and will not seek re-election as chancellor when her fourth term ends in 2021.
Brexit and baby-boomers
The German economy enjoyed stellar growth in 2017 underpinned by brisk domestic and international demand, record-low unemployment and low interest rates.
But Europe's top economy has hit a soft patch this year against a backdrop of slower global growth. The German economy ministry last month lowered its growth estimates and is now pencilling in expansion of 1.8 percent this year and the next.
Clouding the outlook is concern about US President Donald Trump's aggressive "America First" trade agenda which has seen him lock horns with China and the European Union, unsettling Germany's export-reliant companies.
Other outside risks stem from an increased chance of a no-deal Brexit when Britain quits the bloc in March, which could badly disrupt trade, and rising euroscepticism in countries like Italy, the "wise men" said.
"An escalation of the trade conflict, a disorderly Brexit, or a resurgence of the euro area crisis harbour risks for economic development," they warned.
They urged Germany and the European Union to forcefully reject protectionism and stand up for free trade.
Domestically, the experts singled out Germany's ageing workforce as a "major challenge".
German companies are already grappling with a shortage of skilled workers as the baby-boomer generation retires, and the problem is expected to worsen in the years ahead.
To get more people into the workforce, especially women, the experts urged Berlin to encourage flexible working hours and improve childcare options.
Immigrants could likewise help plug the gap, they added, while also advocating a gradual rise in retirement age.
The experts pressed Berlin to make greater strides in preparing Germany for the digital economy, urging investments to improve the country's creaking internet infrastructure.
Berlin should also do more to support tech start-ups and modernize its education system to prepare youngsters for the "digital transformation", they added.