The closest that the federal government could come to penalizing a state for removing a measles vaccination requirement is via 42 USC 264 which authorizes the Surgeon General
to make and enforce such regulations as in his judgment are necessary
to prevent the introduction, transmission, or spread of communicable
diseases from foreign countries into the States or possessions, or
from one State or possession into any other State or possession.
An important limit on that law is that
Nothing in this section or section 266 of this title, or the
regulations promulgated under such sections, may be construed as
superseding any provision under State law (including regulations and
including provisions established by political subdivisions of States),
except to the extent that such a provision conflicts with an exercise
of Federal authority under this section or section 266 of this title.
There are various state-level exemptions (religious or philosophical opposition) which cannot be overridden. However, in the case of a complete lack of requirement for vaccination, there is nothing at the state level to override.
However, without a change in laws, the Surgeon General could not on his own create a regulation that deprives a state of it funding for something – that is beyond the scope of this law (and any regulation authorized by it). The available actions, other than apprehending the infected are limited to
inspection, fumigation, disinfection, sanitation, pest extermination,
destruction of animals or articles found to be so infected or
contaminated as to be sources of dangerous infection to human beings,
and other measures, as in his judgment may be necessary.
That last clause is a pretty big loophole, but the courts will not interpret it to mean "including curtailing funding". Nor can Congress pass a law depriving states of existing funding if they fail to mandate measles vaccination, see NFIB v. Sebelius.
