Weber also told the International Institute of Finance's spring meeting in Tokyo that "Brexit is a time bomb" and Europe was beset with economic dangers.
He said the Italian economy remained in a woeful state, as was Greece's. Britain is due to leave the European Union on March 29, 2019.
"Brexit is a time bomb… and the countdown is on. It will be two years from now… if the British really do leave the customs union and single market there could be a lot of volatility which could impact on the global economy," Weber said.
He said Macron's landslide victory in the second round of the French presidential election did not necessarily change anything and the political risks facing the continent were still "actually quite high."
Weber, who has a PhD in economics, is one of the most respected bankers in the world and was elected to the board of UBS in 2012.
"There is still Italy where it is very unclear that the center will hold. And there is still Greece. Where you find some bright side… there are some downside risks that are not really priced into the market but could derail Europe," Weber said.
In 2014, Weber warned against stronger sanctions on Russia, saying they could have a serious impact on the German economy.
The victory of the 39-year-old pro-business centrist over French nationalist Marine Le Pen, was widely expected and failed to give Europe's stock exchanges any sort of boost.
Macron, who is thought to have hoovered up votes from supporters of Francois Fillon, Benoit Hamon and even the hard-left candidate Jean-Melenchon, defeated the violently anti-EU Le Pen by a margin of 66% to 34%.
But trading on Europe's major bourses remained minimal today with no big jumps at the opening bell, probably because traders had expected his victory.
Macron is France's youngest leader since Napoleon and very little is known about him even now.
Gino Raymond, Professor of Modern French Studies at the University of Bristol, said he thought Macron had got "his work cut out" if he was to save the EU and revive the French economy.
"It's very interesting that the privileged partner is going to be Germany naturally and his key ally is going to Chancellor Merkel… But the harsh facts remain that France itself economically is in a fragile situation. All of the southern European members of the eurozone are still in a fragile situation, although the eurozone is beginning now to enjoy some kind of growth," Professor Raymond told Sputnik.
Professor Raymond said the fundamental problem remained for countries like Italy, Spain, Greece and others was that the Euro was still "over-valued."
"Although Macron is talking tough with regard to Brexit… Macron also knows, that having been a former investment banker, that the City of London as a financial center is actually very useful to the European Union and to the eurozone," Professor Raymond added.
The election of Macron was seen as the second rejection of nationalist, populist ideas in Europe this year.
The Dutch firebrand Geert Wilders and his PVV party failed to make major inroads in the general election in the Netherlands in March. Dutch political scientist Kees van der Pijl told Sputnik at the time, that some of Wilders' themes had been adopted by mainstream parties.
Fillon tried to do that during the French election, by adopting a tough line on immigration, but his campaign was blown off course by a string of corruption allegations.
In the end, Macron, who had not pandered to populist sentiments on immigration or the EU, ended up winning comfortably.
Macron told his supporters Sunday, May 7: "Tonight you won, France won. Everyone told us it was impossible, but they don't know France."