The latest version of the Google app (V.6.11.13 beta), contains strings of code which hint at payments coming to the service soon. Pundits like 9to5Google say uses could include payments for things like Google Express Shopping.
The strings below show that Google Assistant will be able to handle credit cards as most apps do, as well as offering direct links to Google support if assistance is needed. The strings also mention a Google support page which currently isn’t live, but the URL does show that Assistant on Google Home will also have support for payments.
https://9to5google.com/2017/01/16/google-assistant-prepares-for-payments/