Is it a problem to take vicodin with antiviral drugs?

Taking for what? You should always be talking to the prescriber, and it depends on what kind of anti-viral drug. Are we talking Acyclovir or valcyclovir for herpes, or drugs for hepatitis c, or for hiv? Different anti-viral drugs have differing drug interactions. In general, hydrocodone does not have many drug interactions. If it is prescribed, talk to prescriber. If you don't have prescription, don't take it!
No. Vicodin will not interact with antiviral or antiretroviral drugs. The biggest problem with vicodin is that it contains a lot of Acetaminophen (tylenol), and taking too much of that can cause liver problems.