61.23
(3) Must hold at least a third-class medical certificate—
(i) When exercising the privileges of a private pilot certificate, recreational pilot certificate, or student pilot certificate, except when operating under the conditions and limitations set forth in §61.113(i);
(ii) When exercising the privileges of a flight instructor certificate and acting as the pilot in command or as a required flightcrew member, except when operating under the conditions and limitations set forth in §61.113(i);
(iii) When taking a practical test in an aircraft for a recreational pilot, private pilot, commercial pilot, or airline transport pilot certificate, or for a flight instructor certificate, except when operating under the conditions and limitations set forth in §61.113(i); or
113 refers to sport pilot and refers back to 23(c)(3) which allows basic med.
So 3rd class or basic med for check rides unless sport pilot and LSA
Why the medical required? Because the examiner is considered a passenger and you are ACTING as PIC which means currency, medical, etc...