No - you can start and own a U.S. business without an active visa status. Visa status is not required as long as you are a passive owner, as in buying stock or owning real estate.
In order to stay in the U.S. to run a business, you will need legal status.
If you are a student in F-1 status you must have work authorization to be employed at the business. Optional practical training (OPT), the period immediately following graduation, is the most flexible time of F-1 status. After your OPT ends, you will need to find another status to remain the U.S. for the business.
More information on STEM OPT extensions is available on the NAFSA website.
You can only pay yourself if you are authorized for employment by USCIS. In most situations, it makes sense to keep up a series of temporary visas until an opportunity for permanent residence arises.
Our main website offers an overview of unauthorized employment here.
The following visas may be available to entrepreneurs:
H-1B: salaried position related to degree, heavily regulated.
L-1: transfer from employment by affiliated company abroad.
O-1: based on “extraordinary ability” in business or the subject of the business
TN: based on Free Trade Agreement - Canada, Mexico, Chile, Singapore, Australia.
The U.S. Alliance for International Entrepreneurs, co-founded by Attorney Dan Berger, is on a mission to help foreign national students and entrepreneurs grow their businesses in the United States. Visit the USAIE website for news, resources, and services.
Please see this article on our website: "Employment-based Visas: There may be a better way."
USCIS has also created a new web portal for entrepreneurs.
There are immigration initiatives in Congress that could add more visas for entrepreneurs. Follow reputable sites like competeamerica.org to follow and support.
Massachusetts has launched the Global Entrepreneur in Residence Pilot Program, to attract and retain more entrepreneurs in the state's businesses.
FeldThoughts: Announcing the Global EIR Coalition
In September 2013, Columbia Engineering & Columbia Entrepreneurship presented "Immigration & Entrepreneurship: Pathways for International Students to Create New Ventures - and Jobs - in the U.S" (click for video)