The online postage calculator of Deutsche Post states that letters sent as Standardbrief International usually take 6 to 14 working days to reach China. That's about one to three weeks in absolute time.
However, no suche assertion is made about the Postkarte International product. I know that postcards in general have a very low priority with mail carriers, so despite both products costing 90 cents, I would not be surprised if you would have to double that number to get the expected transit time for a Postkarte.
Next time, you could put the card into an envelope and send it as letter, if you want to feel more confident about the transit time.
PS: DHL and Deutsche Post are technically different companies, so I really hope you did not use one of the DHL parcel drops, but a true DP letter box. All those Post spin-offs become quite iffy when they are confused for one another (my favorite being that DHL support does know nothing about DHL Express packages, because they're different companies -.-)