The three are suspected of providing money to Ansar al-Islam that they either raised or donated out of their own pockets, as well as providing other assistance such as courier services, prosecutors said.
The men were identified only as Dieman AI, 39, a Nuremberg resident; Kawa H, 33, from Munich; and Najat O, 43, from the southwestern town of Buehl.
Prosecutors claim Kawa and Najat took orders from one of three alleged Ansar al-Islam members who were arrested in Germany in December on suspicions that they planned to attack then-Iraqi interim prime minister Iyad Allawi during a visit to Berlin.
Prosecutors have said the man, identified only as Ata R, had a leading role in European fundraising for Ansar al-Islam and maintained contact with the group's leaders in Iraq.
One of the three arrested on Tuesday, Najat, is accused of carrying out money transfers to Iraq, allegedly for the group in mid-2004, prosecutors said. They did not detail the sums involved.
No German attacks
"The money served to finance terrorist attacks in Iraq by the Ansar al-Islam group and to secure the organisation's logistical structural foundations," their statement said.
Investigations have turned up no evidence that the money was destined to finance alleged attacks in Germany, it added.
"The money served to finance terrorist attacks in Iraq by the Ansar al-Islam group and to secure the organisation's logistical structural foundations"
Prosecutors said that another 11 people in Germany are under investigation as suspected supporters of Ansar al-Islam but that there was insufficient evidence to arrest them.
Tuesday's arrests were accompanied by searches of 24 properties in parts of Germany and in Basel, Switzerland.
Followers of Ansar al-Islam have been arrested in several European countries for allegedly supporting attacks on US-led forces in Iraq.
Ansar al-Islam was formed in the Kurdish parts of Iraq and is thought to include al-Qaida members who fled the US-led invasion of Afghanistan in late 2002.
Germany has had alleged Ansar al-Islam activists under intense scrutiny for about 18 months.
Last month, an Iraqi man went on trial in Munich on charges that he raised funds for the group and organised travel to Iraq for alleged recruits.
Amin Lokman Mohammed, 31, admitted helping to smuggle Iraqis into Germany but insisted those actions had nothing to do with Ansar al-Islam.