Weapons orders from Saudi Arabia have either been "rejected, pure and simple," or deferred for further consideration, the newspaper said, adding that the information has not been officially confirmed.
The decision was taken on Wednesday by the national security council, a government body that includes Chancellor Angela Merkel, Vice Chancellor Sigmar Gabriel and seven other ministers, it said.
"According to government sources, the situation in the region is too unstable to ship arms there," added the daily.
Saudi Arabia follows a strict and highly conservative form of Islam, and as home to some of its holiest sites plays a key role as a spiritual leader for Sunni Muslims and mediator in the Middle East.
Its importance was made clear on Saturday when world leaders converged on Riyadh to offer condolences following the death of King Abdullah, including Britain's prime minister and France's president.
Germany was represented by former president Christian Wulff.
The kingdom is "one of the most important clients of Germany's arms industry," with 360 million euros ($400 million) of arms shipments authorised in 2013, Bild said.
But it has also come under fire from human rights groups for its harsh treatment of religious minorities and women, as well as the lack of transparency in its legal system.
A survey carried out for Bild found that 78 percent of Germans believe Berlin should stop selling arms to Saudi Arabia -- and a further 60 percent want to break off trade ties all together -- due to human rights violations.