Sure it is. And court decisions have backed that up.
It's not worded the same as the first, but neither are amendments three through eight -- and they are restricted to the federal government (or were, until the passage of the 14th amendment).
"Another important factor in the small arms-control debate is federalism. Like all the other Bill of Rights Amendments, the Second Amendment was originally added to the Constitution to limit the power of the federal government only. Both the 1876 decision of United States v. Cruikshank and the 1886 decision of Presser v. Illinois recognized this and explicitly stated the Second Amendment limits the power of the federal government only".
"The basic liberties of the Bill of Rights did not become applicable to the states until after the adoption of the Fourteenth Amendment. Among other things, the Fourteenth Amendment prohibited the states from depriving "any person of life, liberty, or property, without due process of law." Through a tortuous, decades-long process, the Court eventually adopted the view that certain fundamental liberties in the Bill of Rights could be incorporated through the due process clause and turned into limits against the power of the states also. In separate decisions, the right of free speech, the right to freely exercise one's religion, the right to be free from unreasonable searches and seizures, and so on, were made applicable to the states by the Justices."
"The Second Amendment right to bear arms, however, has never been incorporated by the Court into the Fourteenth Amendment. The result is that today the Second Amendment, whatever it may mean, operates to restrict only the power of the federal government. The states remain unfettered by the Amendment's limitations. They remain essentially free to regulate arms and the right to bear them as they choose, in the absence of strictures in their own state constitutions and laws."
-- time.com