Hamburg is the first German state to have started issuing payment cards to asylum seekers instead of cash, after state leaders largely agreed on the new way to provide welfare benefits.
Since Thursday, newly arrived refugees who are entitled to benefits have been receiving the prepaid card, a spokesman for the social welfare authority said on Thursday.
Each adult is to receive a monthly credit of €185 ($199) on the card, which could be used to buy and pay for everyday items. Benefits for children would also be credited to a parent's card.
Earlier this month, 14 of Germany's 16 federal states agreed on the new card format to be introduced this summer.
The switch is partly intended to prevent migrants from transferring welfare benefits back to relatives or friends in their home country, an issue that has been raised by some German politicians.
It should also streamline the distribution of benefits and ease the administrative burden on local government authorities.
The two other states, Bavaria and Mecklenburg-Vorpommern, also intend to introduce a card for migrants but will pursue their own standard.
Pilot projects are already under way at municipal level in several federal states.
Cash withdrawals of up to a maximum amount of €50 per month plus €10 for each child would reportedly also be possible.
"The card can be used both as a card and via a corresponding app on the smartphone in all shops and service providers that accept card payments," the welfare authority stated.
However, it is not possible to use the card abroad or in online shops.