With the referendum on whether the U.K. should "Brexit" too close to call, "it creates huge uncertainty," Weber, who was president of the German Bundesbank from 2004-2011, told CNBC's "Street Signs" in an exclusive interview.
"You already see that British assets have a risk premium attached to them over recent months, including the pound," he said.
From a peak of around $1.5882 in mid-June of 2015, the pound is now fetching around $1.4431, losing more than 9 percent of its value against the greenback.
Concerns about the referendum may factor in to the Fed's decision-making on a rate hike, which has been clearly signaled as likely in June or July.
"I think June, because of the British poll, is less likely to some degree than a July move," Weber said.
But either way, he believes a rate hike is likely a done deal.
"Whether it's July or June, for domestic reasons, purely domestic reasons, I think the U.S. is ready for a rate hike and the Fed has signaled that," he said. "The rest is tactical decisions on when to do that best rather than whether to do it or not to do it."
While some analysts believe the Fed is less likely to move when no press conference is scheduled, Weber doesn't believe it will be a factor.
A press conference is scheduled to follow the June 14-15 meeting, but not after the July 26-27 meeting.
"Monetary policy is not as much about the decision of the day. It's really more about forward guidance and about informing markets what's ahead and that's a much more medium term view," he said. "The Fed has done most of that. It might actually be helpful to decouple the ability to move rates from the ability to have a press meeting," he said. "It ties your hands in the market in an unfortunate way."
If there's no June hike, the Fed's language will be "pretty clear," Weber said. "I think the market then will almost perfectly price a July rate hike if the language is pretty straight forward."
But Weber was skeptical on the efficacy of a negative interest rate policy, saying that while negative rates may have more pronounced effects in small open economies, such as Denmark, Sweden and Switzerland, in large economies, such as the eurozone and Japan, the impact could "easily go the other way."
"What you usually want to do with lowering rates or going into negative territory, you want to boost consumption and reduce savings," he said. But in a negative-rate environment, people may become concerned about their ability to earn a decent pension, he said.
"That ability goes down dramatically in a negative interest rate environment so they might just overall be concerned about their level of pension and start saving more rather than saving less and consuming less rather than consuming more," Weber said.
Within the eurozone, UBS has repriced some of its products in response to negative rates, he said.
"Credit is getting more expensive in those areas where you can actually increase prices for those products," he said.
—By CNBC.Com's Leslie Shaffer; Follow her on Twitter @LeslieShaffer1
