From the Gmail web interface, create a rule to give it a label of your choice and skip the inbox. Then, from the Gmail Android app, change the settings for that label to not notify you.
In more detail, the first part is:
- Log into Gmail in a browser, and click the settings button (gear icon).
- Click the Filters tab, then Create a new filter at the bottom.
- Set the settings for the filter: in this case, use the From field.
- Click the search button (magnifying glass) to check your filter, or go straight to Create a filter with this search.
- Put a tick in the Skip the inbox (Archive it) checkbox, and another in Apply the label and choose the label you want or create a new one from the drop-down.
- Click Create filter.
Then, starting from the main screen (folder view) of the Gmail app:
- Click the overflow menu (three dots in the top-right)
- Choose Manage labels
- Choose the label you just set in the filter
- Make sure Label notifications is turned off.