An air carrier that I have worked for specifically addresses this issue in their General Operations Manual—which is accepted by the FAA. The manual gives the following requirement:
Flight Restrictions After Blood Donations
Flight personnel shall not participate in any capacity as flightcrew members for a period of 24 hours after donating more than one-half pint of blood.
Note that this portion of this manual is accepted by the FAA, not approved.1
One unit of blood is generally 470-500 mL, or one pint. The one-half pint specified above half of a regular unit of blood. According the the Red Cross, a typical donation is about one pint, or one unit.
The FAA also publishes the Guide for Aviation Medical Examiners. I am not an AME, nor am I fully familiar with the Guide or how to interpret it. However, I understand that the following table shows that outside the listed time-frames, an applicant for an airman's medical certificate could be considered medically fit for flight duty:
1 The terms Approved and Accepted mean specific things to the FAA. See 8400.10, Vol 3, Ch 15, Sec 1:
Approved: When approved is used to describe a document, manual, or checklist, it means that a regulation requires FAA approval and that the FAA has evaluated and specifically approved the document, manual, or checklist.
Accepted: Accepted is used to describe a document, manual, or checklist that does not have, or is not required to have, FAA approval. Only a portion of an operators manuals are required to have FAA approval. The remaining portions are accepted by the FAA. Operators are required to submit the entire general manual to the FAA for review. If the FAA concludes that an accepted section of the general manual is not in compliance, the FAA must formally notify the operator of the deficiency. Upon notification, the operator must take action to resolve the deficiency.