"The Congress shall have power...
To regulate commerce with foreign nations, and among the several states, and with the Indian tribes..."
Congress has passed such laws, authorizing the President to impose economic sanctions banning trade with countries which pose "any unusual and extraordinary threat, which has its source in whole or substantial part outside the United States, to the national security, foreign policy, or economy of the United States, if the President declares a national emergency with respect to such threat." (50 U.S. Code § 1701, 1702, and so on http://www.law.cornell.edu/uscode/text/50/1701).
The President recently used these powers to restrict trade with certain entities in Russia, to put pressure on Russia to stop providing support for separatists in the Ukraine: http://www.treasury.gov/resource-center/sanctions/Programs/D...
So, it's not quite "just like that". The President must declare a state of national emergency (which he did in Executive Order 13660 in March http://www.treasury.gov/resource-center/sanctions/Programs/D..., expanded in EO 13661 http://www.treasury.gov/resource-center/sanctions/Programs/D..., and expanded further in EO 13662 linked above), and can only impose sanctions directly related to that national emergency.
Ukraine is a country which agreed to disarm itself of nuclear arms when it split apart from the USSR, in exchange for an agreement that nuclear armed nations like the US, Russian Federation, and others would respect the independence and sovereignty of Ukraine and not use force against the Ukraine. http://en.wikipedia.org/wiki/Budapest_Memorandum_on_Security... The invasion of Russian and annexations of Crimea is a direct violation of this agreement, and a very worrying trend for nuclear non-proliferation. Russia's further involvement invading the east of Ukraine (under the guise of simply supporting an "organic" separatist movement) is further seriously troubling.
Hope that helps explain the situation. The President cannot simply order any private company to suspend working with other companies, but can if he declares a national emergency and the sanctions are directly related to that national emergency.