The federal government approves all of the permits needed to make beer.
What this means is if a new brewery wants to open, they must get permission from the government. It also means that if a brewery wants to start making a new beer, they must get permission from the government.
The Alcohol and Tobacco Tax and Trade Bureau (TTB) is mostly closed right now thanks to the government shutdown. According to Yahoo News, they will continue to process taxes from existing permit holders. But, they are not accepting any new applications.
The has little impact on large, established companies like Anheuser-Busch. But, it makes life very tough for small, craft brewers.
There are many craft breweries that cannot open until their permits are processed. This is the issue for Washington D.C's Blue Jacket Brewery. The brewery tells NBC Washington that it is close to opening, but cannot do so until they have the proper permits. They won't get those permits until the government shutdown ends.
Breweries that are currently open are also affected. Craft brewers thrive off of releasing new beers. But, they cannot get approval for any new beer until the shutdown is over.