Mr Maas made the provocative suggestion in an opinion piece for Handelsblatt, a German business paper.
He said: “Where the US crosses red lines, we as Europeans must counterbalance.
“It is therefore essential that we strengthen European autonomy by setting up payment channels independent of the USA, creating a European Monetary Fund and building an independent Swift system.”
The Swift system is a massive messaging network used by banks and other financial institutions.
An independent European system would make European companies less vulnerable to US sanctions, but would likely anger the Trump administration.
President Trump has threatened action against companies which carry on doing business with Iran, as the US reimposes sanctions over the country’s controversial nuclear programme.
The US leader announced the US would withdraw from the Iran nuclear deal in May.
The deal had been intended to stop Iran developing nuclear weapons in return for lifting crippling sanctions.
However President Trump claimed Iran was continuing to develop ballistic missiles and had been supporting terror groups across the Middle East.
On August 7 President Trump Tweeted: “Anyone doing business with Iran will not be doing business with the United States.”
The US leader’s first round of sanctions against the Middle Eastern nation was reimposed earlier this month, while a second is due to come into effect in November.
The UK, France, Germany, Russia and China, who also signed the Iran nuclear deal, are continuing to support the accord.
When the US announced its withdrawal, the UK, France and Germany released a joint statement expressing “regret and concern”.
Mr Maas commented on the situation in Handelsblatt, stating: “The devil is in a thousand details.
“But every day the deal persists is better than the high-explosive crisis that otherwise threatens the Middle East.”
He has previously stated: “The US under Donald Trump will not play the same role that it has in the past.”