A much less clear question is what do we mean by "approved", and who is allowed to approve it?
The authority (CAA, FAA, Transport Canada, etc.) - whoever approved the aircraft.
Sec. 23.1581
General.
(a) Furnishing information. An Airplane Flight Manual must be furnished with each airplane, and it must contain the following:
.......
(b) Approved information.
(1) Except as provided in paragraph (b)(2) of this section, each part of the Airplane Flight Manual containing information prescribed in Secs. 23.1583 through 23.1589 must be approved, segregated, identified and clearly distinguished from each unapproved part of that Airplane Flight Manual.
........
This includes "Emergency Procedures" and "Normal Procedures" sections, from which manufacturer's checklists are derived.
If you are ramp checked (or worse, on the witness stand) and asked to produce the checklist you referred to for the flight, it would be helpful to you if the one you produced was obviously approved by the authority. The one you'll find in the Flight Manual is.
That said, I agree that there are a few aircraft flying out there which predate this requirement (pre 1949). I suppose with those, you just do your best if the POH provides no checklist.