The Sueddeutsche Zeitung reported on its website that weapons including tanks and machine guns are to be delivered to countries including the United Arab Emirates, Saudi Arabia and Algeria.
Jordan, Oman and Kuwait would also receive German weaponry.
But critics rounded on the government's decision, with Jan Van Aken, a deputy from the far-left party Die Linke, questioning the delivery to Qatar in particular.
Germany's development aid minister Gerb Mueller had in August directly accused Qatar of financing the Islamic State group, although Berlin had said it regretted any offence caused in Doha over the comment.
Qatar has repeatedly denied the charges, and has since joined the United States in conducting air strikes against IS jihadists.
The opposition also took Vice Chancellor and Economy Minister Sigmar Gabriel to task over the decision, accusing him of bending to the arms lobby.
As recently as August, Gabriel had pushed for rules to be tightened on arms exports particularly to countries with poor human rights records, and had called for deliveries to Saudi Arabia to end.
Under German law, arms exports to countries outside the European Union and non-NATO allies are banned, although exceptions can be made on a case-by-case basis.
In 2013, Berlin authorized a total of 5.8 billion euros worth of armament shipments, 62 percent of which were destined for non-NATO states such as Algeria, Qatar and Saudi Arabia.