No, you don't have to file.
- you are a resident of Virginia, part-year resident, or a nonresident, and
- you are required to file a federal income tax return, and
- you have Virginia adjusted gross income equal to or greater than: Single or married filing separately $11,950 or Married filing jointly $23,900.
However, you should file if you are due a refund of the VA state income taxes you paid. See How do I file a part-year state return?