The funds will be made available as long-term loans for the International Monetary Fund's Poverty Reduction and Growth Trust (PRGT).
In April, IMF officials said they had received pledges of a combined $11.7 billion from Australia, Japan, Canada, France and Britain to replenish the PRGT. The United States has not yet pledged any money for the programme.
"With the funds ... low-income countries can receive greatly discounted loans and bridge liquidity bottlenecks," the German finance ministry said.
It added that Germany will provide a total of 8.7 billion euros for international aid measures in 2020 and 2021. ($1 = 0.8752 euros)