Do you pay federal income tax on an inheritance?

You most likely won't have Federal Income tax on your inheritance. More because generally the tax due, (if any as there are now a number of exemptions) is paid under the Estate & Gift Tax provisions, which interlink with the income tax provisions. (Yes, there are any number of taxes due on gifts and winnings, or just the finding of money. Also, always keep in mind the State income tax implications may be different than the Federal.

The whole Gift, Estate & Inheritance taxes arena can be a complex field, requiring calculating lifetime exemptions, etc. Review the link provided and the further links to the sections that seem relevant to your situation.