Google announced in the Google My Business Help forums and on Twitter that now restaurants can add and edit their menu listings directly in the Google My Business console.

Allyson Wright, Community Manager, Google My Business wrote:

Here is where the info tab would show the menu link if you have access to this feature:

Then when you click on it, it would launch this screen:

Not ever business will have this option, you need to be considered some sort of location that has menus, like restaurants. Plus, it is only available for those who already are connected to a third party provider and for listings in English speaking locals.

Late 2016, Google gave businesses the ability to control their menu links and last year they began showing up in the local panels but menus themselves have been in these results since 2014 and earlier.

Forum discussion at Google My Business Help forums and on Twitter.